Problem 12.1: The potential energy of a body of mass 20.0 kg is 3.5 kJ. What is the height of the body from the ground? If a body of mass 20 kg is moving at a velocity of 50 m/s, what is its kinetic energy?
Problem 12.2: Nitrogen gas, 0.1 cubic meters in volume, is confined in a cylinder at a pressure of 200 kPa, and a temperature of 300 K is expanded at constant temperature to double its volume. What is the work done by the gas on the piston? Assume that nitrogen behaves as an ideal gas.
Problem 12.3: A man circling the earth in a spaceship weighed 300 N at a location where the local gravitational acceleration was 3.35 m/s2. Calculate the mass of the man and his weight on the earth where the gravitational acceleration is 9.81 m/s2.
Problem 12.4: A spherical balloon of diameter 0.5 m contains gas at 1 bar and 300 K. The gas is heated and the balloon is allowed to expand. The pressure inside the balloon is found to vary linearly with the diameter. What would be the work done by the gas when the pressure inside reaches 5 bar.
Problem 12.5: A car having a mass of 1200 kg is running at a speed of 60 km/h. What is the kinetic energy of the car in kJ? What is the work to be done to bring the car to a stop?
Problem 12.6: A body of mass 50 kg is lifted through a distance of 15 m. What is the work done? If it took 2 min to lift the mass, calculate the power.
Problem 12.7: A 100-kg ball initially at a height of 15 m is dropped to the ground. (a) Find the initial potential energy and kinetic energy of the ball. (b) Find the final potential energy and kinetic energy of the ball. (c) If the initial potential energy is converted to heat and the entire heat is transferred to 100 kg of water, what would be the temperature rise of water?
Problem 12.8: A man whose weight is 700 N takes 2.5 minutes for climbing up a staircase. What is the power developed in him, if the staircase is made up of 20 stairs, each 0.18 m in height?
Problem 12.9: A balloon filled with hydrogen lifts a mass of 150 kg including its own mass. If the density of hydrogen is 0.09 kg/m3 at the prevailing conditions, what would be the volume of the balloon?
Problem 12.10: Nitrogen gas is confined in a cylinder and the pressure of the gas is maintained by a weight placed on the piston. The mass of the piston and the weight together is 100 kg. The acceleration due to gravity is 9.81 m/s2 and the atmospheric pressure is 1.01325 bar. Assume that the piston is frictionless. Determine the following: (a) The force exerted by the atmosphere, the piston and the weight on the gas if the piston is 200 mm in diameter (b) The pressure of the gas (c) If the gas is allowed to expand pushing up the piston and the weight by 500 mm, what is the work done by the gas in joules? (d) What is the change in the potential energy of the piston and the weight after the expansion in part (c)?
Problem 12.11: A body of mass 20 kg is dropped from a height of 15 m. What is the potential energy of the body at the time of its release? Assume that the potential energy gets converted into kinetic energy when the body strikes the ground. At what velocity does it strike the ground?
Problem 12.12: Water at a rate of 1 × 10-3 m3/s is pumped from a storage tank into a tube of 30 mm diameter. (a) Determine the kinetic energy of water in J/kg. (b) If the water is discharged into a tank at a height of 15 m, what is the increase in the potential energy of water from that in the original tank?
Problem 12.13: A spherical balloon of diameter 0.5 m contains a gas at 1 bar and 300 K. The gas is heated and the balloon is allowed to expand. The pressure inside the balloon is directly proportional to the square of the diameter. What would be the work done by the gas when the pressure inside reaches 5 bar?
Problem 12.14: The steam supplied to an engine liberates 5000 J of heat. If the engine efficiency is only 40 percent, to what height a body of mass 10 kg can be lifted using the work output from the engine?
Problem 12.15: A vertical cylinder is separated into two compartments by means of a piston, the compartments being filled with two different gases. If the whole cylinder were filled with any one of these gases, it would support a pressure equal to three eighth of the weight of the piston. What would be the position of the piston separating the two gases?
Problem 12.16: A balloon which was originally empty is being filled by hydrogen from a cylinder at a constant temperature of 300 K. The atmospheric pressure is 1.01325 bar. What is the work done by the balloon-cylinder system when the balloon attains a spherical shape with a diameter of 6 m?
Problem 12.17: Five kilograms of CO2 gas is contained in a piston-cylinder assembly at a pressure of 7.5 bar and a temperature of 300 K. The piston has a mass of 6000 kg and a surface area of 1 m2. The friction of the piston on the walls is significant and cannot be ignored. The atmospheric pressure is 1.01325 bar. The latch holding the piston in position is suddenly removed and the gas is allowed to expand. The expansion is arrested when the volume is double the original volume. Determine the work appearing in the surroundings.
Problem 12.18: An elevator is initially resting at a height of 7.5 m above the base of the elevator shaft. It is then raised to a level of 75 m above the base when the cable holding it breaks. It falls freely to the base where it is brought to rest by a strong spring. The mass of the elevator is 2500 kg and the acceleration due to gravity is 9.81 m/s2. Neglecting the effect of friction, calculate (a) The potential energy of the elevator in its initial position (b) The potential energy of the elevator in its highest position (c) The work done in raising the elevator (d) The kinetic energy and velocity of the elevator just before it strikes the spring (e) The potential energy of the spring when the elevator rests on it.
Problem 12.19: Water is being vaporized by passing an electric current of 0.5 A from a 12 V supply through a resistance immersed in saturated water at atmospheric pressure. If the current is passed for 5 minutes and water evaporated is 0.798 g, calculate the change in molar internal energy and molar enthalpy during this process. Assume that the water vapour behaves ideally.
Problem 12.20: Liquid CO2 at 233 K has a vapor pressure of 1.005×103 kPa and a specific volume of 0.9×10-3 m3/kg. Assume that CO2 is a saturated liquid at these conditions and its enthalpy is zero. The latent heat of vaporization of CO2 is 320.5 kJ/kg and the specific volume of saturated vapor is 38.2×10-3 m3/kg. Calculate the internal energy of saturated liquid and both internal energy and enthalpy of saturated vapor.
Problem 12.21: A gas expands from an initial volume of 0.2 m3 to a final volume of 0.4 m3 in a reversible steady flow process. During the process the pressure varies as
P=5\times10^5V+7\times10^4where P is in N/m2 and V is in m3. The inlet line is 4 m below the outlet line, and the gas enters with a negligible velocity. The internal energy of the gas decreases by 30 kJ during the process. Determine the heat transferred.
Problem 12.22: Liquid water at 373 K and 101.3 kPa has an internal energy of 420 kJ/kg on an arbitrary basis. The specific volume at these conditions is 1.04×10-3 m3/kg. The water is brought to the vapor state at 473 K and 700 kPa. At this condition, its specific volume is 0.3 m3/kg and its enthalpy is 2844 kJ/kg. Calculate the enthalpy of the liquid and the changes in internal energy and enthalpy accompanying the vaporization process.
Problem 12.23: A sample of 10 g of liquid benzene at its boiling point is vaporized using a 12 V, 0.5 A electric supply. The normal boiling point and the latent heat of vaporization of benzene are 353.2 K and 30.8×103 kJ/kmol respectively. Determine (a) The change in internal energy (b) The time required for complete vaporization.
Problem 12.24: The heat capacity of carbon dioxide gas is given by
C_P=26.540+42.454\times10^{-3}T-14.298\times10^{-6}T^2where CP is in J/mole K and 7 in K. (a) Find the amount of heat needed to heat one mole from 350 to 450 K. (b) Find the constants for Cp in cal/mol °C and T in °C.
Problem 12.25: Carbon dioxide has a molal heat capacity of Cp = 26.54 + 42.454×10-3 T 14.298×10-6 T2 where Cp is in J/mol K and T in K. (a) Calculate the heat capacity at 400 K. (b) Calculate the mean heat capacity between 400 and 300 K. (c) Calculate the heat requirement for heating 88 kg of the gas from 300 K to 400 K.
Problem 12.26: The molal heat capacity of CO2 gas is given by Cp = 26.540 + 42.454×10-3 T – 14.298×10-6 T2 where Cp is in kJ/kmol K and T in K. Calculate the following: (a) The mean molal heat capacity between 500 and 1000 K (b) The heat required to raise the temperature of 200 m3 per hour of CO2 gas at STP from 500 to 1000 K.
Problem 12.27: A 5 kg mass of a gas undergoes a process in which its temperature rises from 10°C to 30°C. The specific heat of the system is
C_P=3.505+\frac{263.9}Twhere Cp is in kJ/kg K and 7 is in K. Determine the following: (a) The heat interaction (b) The mean heat capacity of the system.
Problem 12.28: The heat capacity of HCl for the temperature range of 300 to 1500 K is given by CP = 28.194 + 1.805×10-3 T + 1.513×10-6 T2 where Cp is in kJ/kmol K and T in K. Calculate the following: (a) The mean heat capacity at 1300 K with reference to 300 K (b) The enthalpy change of HCl when it is heated from 300 K to 1300 K.
Problem 12.29: Determine the specific heat of a gas at 800 K for which Cp varies with temperature as Cp = a + bT+ cT2 where a, b and c are constants. The following data are available.
| T (K) | 300 | 600 | 900 |
| CP (kJ/kmol K) | 28.788 | 30.417 | 32.033 |
Problem 12.30: The heat capacity of ethylene gas at different temperatures are given below.
| T (K) | 298 | 500 | 700 | 1000 |
| CP (kJ/kmol K) | 43.6 | 63.5 | 78.5 | 94.5 |
(a) Fit the data into an equation of the form Cp = a + bT + cT2. (b) Calculate the heat required to raise the temperature of one mole of ethylene gas from 400 to 1000 K.
Problem 12.31: Calculate the amount of heat given off when 5 m3 of SO3, gas at STP cools from 773 K to 400 K at a constant pressure of 101 kPa. The heat capacity is given as Cp= a + bT + CT2 where a, b and c are constants. The values of the constants are: a = 34.33, b×103 = 42.86 and c×106 = -14.298. Cp is in kJ/kmol K and T in K.
Problem 12.32: The heat capacity of silicon carbide is given by Cp = 37.221 + 1.22×10-2 T 1.189×105 T-2 where Cp is in kJ/kmol K and T is in K. Estimate the following: (a) The mean heat capacity of silicon carbide in the range of 0 to 1000°C (b) The enthalpy change in silicon carbide in the temperature range between 0 to 1000°C.
Problem 12.33: A gas mixture contains species A (MW = 30) 15 %, species B (MW = 45) 45 % and species C (MW = 80) 40 % by weight. Calculate the quantity of heat necessary to heat one kilomole of the mixture from 300 K to 2700 K. The constants of the molar heat capacity equation Cp = a + bT + cT2 are as follows where Cp is in kJ/kmol K and T is in K.
| Species | a | b | c×103 |
| A | 25 | 0.05 | -0.01 |
| B | 30 | 0.009 | -0.05 |
| C | 21 | 0.08 | -0.001 |
Problem 12.34: The gas leaving a pyrites roaster in a sulphuric acid plant has the following composition. SO2 7.00 %, O2 = 10.50 %, SO3 = 0.80 %, N2 = 81.70 %. The heat capacity of the gases varies with temperature as given below where Cp is in kJ/kmol K and T is in K.
O2: Cp = 25.74 + 12.987×10-3 T – 3.864×10-6 T2; N2: Cp = 27.03 + 5.815×10-3 T – 0.289×10-6 T2; SO3: Cp = 34.33 + 42.86×10-3 T – 14.298×10-6 T2; SO2: Cp = 25.74 + 57.96×10-3 T – 38.11×10-6 T2
Calculate the enthalpy of the gas mixture at 750 K with reference to a base temperature of 298 K.
Problem 12.35: The analysis of natural gas showed the following: Methane, 40.00 %; Hydrogen, 40 %; carbon monoxide, 4.0 %; carbon dioxide, 3.0 %; oxygen, 2.0 % and the rest nitrogen. A 1-kw heater is used to supply heat to the gas so that its temperature increases by 0.2 ˚C. Estimate the flow rate of the gas in cubic metres per minute at 300 K and 100 kPa. The specific heats of the gases in kJ/kmol K are 35.91 for methane, 28.95 for hydrogen, 29.25 for carbon monoxide, 37.31 for carbon dioxide, 29.47 for oxygen and 29.24 for nitrogen.
Problem 12.36: One kg of ice at 273 K and 5 kg of water at 300 K are mixed and kept in an open container till all the ice melts and the temperature of the mixture becomes 295 K. Given that the heat of fusion of ice is 335 kJ/kg, calculate the heat added or removed to or from the water and ice.
Problem 12.37: One kilogram of ice at 0 °C is heated so that it is completely converted to steam at 150 °C and 101.3 kPa. What is the enthalpy change accompanying the process? The heat of fusion of water at 101.3 kPa and 0 °C is 335 kJ/kg and heat of vaporization of water at 101.3 kPa and 100°C is 2256 kJ/kg. The heat capacity equation of liquid water is Cp = 18.296 + 47.212×10-2 T – 133.88×10-5 T2 + 1314.2×10-9 T3 and the heat capacity equation of water vapour at 101.3 kPa is Ср = 30.475 + 9.652×10-3 T + 1.189×10-6 T2 where T is in K and specific heat is in (kJ/kmol K).
Problem 12.38: The vapor pressure of water at 473 K is 1554.3 kPa. The normal boiling point of water is 373 K. Determine the latent heat of vaporization of water assuming that it is independent of temperature.
Problem 12.39: The vapor pressure of ethyl ether at 273 K is 25 kPa and at 293 K is 63.5 kPa. Estimate the latent heat of vaporization of ether in kJ/kg in this temperature range.
Problem 12.40: Using the Watson equation, calculate the latent heat of vaporization of n-butane at 373 K given that the heat of vaporization at the normal boiling point of 272.7 K is 385 kJ/kg. The critical temperature of n-butane is 425 K.
Problem 12.41: Using Trouton’s rule, find the approximate heat of vaporization of benzene boiling at 80°C.
Problem 12.42: The vapour pressure of zinc is given by the Clapeyron equation
\log\left(P^S\right)=-\frac{6160}T+8.1where pressure is in mm Hg and temperature is in K. Estimate the heat of vaporization of zinc at the normal boiling point of 1180 K, and compare the result with the value estimated using the Kistyakowsky equation.
Problem 12.43: Calculate the enthalpy of zinc vapour 1500 K and standard atmospheric pressure with reference to the solid at 273 K. The melting point and the boiling point of zinc at atmospheric pressure are 592 K and 1180 K respectively. The mean heat capacity of the solid between 273 K and 592 K = 0.441 kJ/kg K; the mean heat capacity of liquid = 0.458 kJ/kg K; the mean heat capacity of the vapour from 1180 K to 1500 K = 20.874 kJ/kg K; the heat of fusion = 6972 J/g-atom. Use the Kistyakowsky equation.
Problem 12.44: Methyl chloride is obtained from the vapor-phase catalytic reaction between methanol and hydrogen chloride. The liquid methanol is vaporized in a separate vaporizer, and the vapors are continuously mixed with HCl gas in equimolar proportions. The mixed gases are preheated in a tube furnace to 200 °C before entering the catalytic reactor. The heat capacity of liquid methanol 2.62 kJ/kg K. The mean heat capacity of methanol vapor is 53.47 kJ/kmol K. The mean heat capacity of HCl gas is 41.70 kJ/kmol K. The normal boiling point of methanol is 337.9 K. The heat of vaporization of methanol at 101.3 kPa is 35.3 kJ/mol. On the basis of 400 kg/h of alcohol feed at 25 °C, find the following: (a) The heat duty of methanol vaporizer operating at one standard atmosphere (b) The heat duty of the tube furnace if the methanol vapor enters saturated at 1 atm, the HCl enters at 30 °C, no chemical reaction occurs in the furnace, and heat losses are negligible.
Problem 12.45: The following table gives the vapor pressures of benzene and water. Plot the reference temperature vapor pressure curve with the logarithm of the vapor pressure of benzene on the y-axis and the logarithm of the vapor pressure of water on the x-axis.
| T (K) | 288.6 | 299.3 | 315.4 | 333.8 | 353.3 | 377.0 | 415.7 | 452 |
| P_B^S (kPa) | 8.0 | 13.3 | 26.7 | 53.3 | 101.3 | 202.7 | 506.6 | 1013.0 |
| P_W^S (kPa) | 1.8 | 3.4 | 8.3 | 23.1 | 49.0 | 116.3 | 382.5 | 980.0 |
(b) Determine the vapor pressure of benzene at 373 K. (c) Determine the latent heat of vaporization of benzene at 298 K given that the latent heat of vaporization of water at 298 K is 2443 kJ/kg. Compare your result with the experimental value of 434 kJ/kg.
Problem 12.46: A steam-jet ejector is used to entrain saturated water vapor at 25 kPa (H = 2618.2 kJ/kg) leaving an evaporator by high-pressure saturated steam at 1000 kPa (H = 2778.1 kJ/kg). It is estimated that with every kilogram of high-pressure steam, 0.75 kg of the vapor from the evaporator can be entrained. If the mixed stream leaving the ejector is at 100 kPa what is its temperature?
Problem 12.47: A valve on a well-insulated steam pipe carrying saturated steam at 1000 kPa is found leaking. The temperature of the steam escaping from the leak is measured to be 398 K. Determine the quality of steam flowing through the pipe.
The following data are taken from steam tables: the enthalpy of saturated vapor at 1000 kPa =2778 kJ/kg, the enthalpy of saturated liquid at 1000 kPa = 763 kJ/kg and the enthalpy of superheated steam at 398 K and 101.3 kPa = 2726 kJ/kg.
Problem 12.48: Wet steam containing 5 % by weight of liquid at a pressure of 500 kPa is mixed at a rate of 1 kg/s with superheated steam at 500 kPa and 473 K (H = 2855 kJ/kg) to obtain dry saturated steam at 500 kPa (H1 = 640 kJ/kg; HV =2749 kJ/kg). Determine the rate of addition of superheated steam if mixing is done adiabatically.
Problem 12.49: An evacuated tank is connected to a pipe carrying steam at 1400 kPa and 598 K (enthalpy = 3097 kJ/kg) through a valve. The valve is opened and the tank fills with steam until the pressure is 1400 kPa, and then the valve is closed. Assume that the process is adiabatic and the kinetic and potential energies are negligible. Determine the final temperature of the steam.
Problem 12.50: Using steam tables, find the enthalpy change when (a) one kilogram of water is heated from 293.15 to 323.15 K at 101.3 kPa and (b) when one kilogram of water at 293.15 K is heated and vaporized at 200 kPa.
Problem 12.51: A closed tank contains 10 kg of water in equilibrium with 2 kg of steam at 349 K. Heat is added until 8 kg of the water is vaporized. (a) What was the original pressure? (b) What is the final pressure? (c) How much heat was added?
Problem 12.52: A mixture of saturated steam and saturated water is contained in a rigid tank of volume 0.1 m3 at a pressure of 2 bar. The liquid occupies 10 % of the total volume. How much heat must be added in order that the tank contain only saturated steam? What will be the pressure in the tank?
Problem 12.53: A steam boiler is one-fourth filled with liquid water at 101.3 kPa and 373.15 K and three-fourth filled with steam. If it is brought to a pressure of 6817 kPa with all the valves closed, how much heat must be supplied in kJ per kilogram of water in the boiler?
Problem 12.54: A vessel of volume 1 m3 initially contains one percent by volume saturated liquid water and the rest saturated vapor at 1 bar. How much heat is to be supplied so that the vessel gets filled with vapor?
Problem 12.55: A steam boiler of volume 2.3 m3 initially contained 1.7 m3 liquid water in equilibrium with 0.6 m3 of vapor at 100 kPa. The boiler is heated keeping the inlet and discharge valves closed. The relief valve is set to lift when the pressure in the boiler reaches 5500 kPa. Determine the amount of heat supplied to the contents in the boiler before the relief valve lifts.
Problem 12.56: A cylinder fitted with a piston has a volume of 0.1 m3 and contains 0.5 kg of steam at 500 kPa. How much heat is to be supplied to bring the temperature of the steam to 823 K, keeping the pressure constant? What is the work done in the process?
Problem 12.57: Fifty kilograms of NH4NO3 is dissolved in 108 kg of water at 298 K. Find (a) the heat absorbed if the process is isothermal and (b) the temperature of the mixture if the dissolution is carried out adiabatically. Take the heat capacity of the mixture to be 3.35 kJ/kg K.
Problem 12.58: The heat of the formation of LiCl is −408.610 kJ/mol at 298 K. The heat of solution for 1 mol LiCl in 12 mol water is −33.614 kJ at 298 K. Calculate the heat of formation of LiCl in 12 mol water at 298 K.
Problem 12.59: One hundred kilograms of pure H2SO4 is mixed with 110 kg of water at 25 °C and 101.3 kPa. Calculate the following: (a) The heat evolved under isothermal conditions (b) The final temperature of the mixture if it was formed under adiabatic conditions. Assume the heat capacity of the final mixture is 2.5 kJ/kg K.
Problem 12.60: What temperature will be attained when a 20 mole percent ethanol-water mixture is adiabatically formed from the pure liquids at 298 K? The heat of mixing for 20 mole percent ethanol-water at 298 K is -758 J/mol. The mean heat capacity of a 20 mole percent solution of alcohol in water at 298 K is 97.65 J/mol K.
Problem 12.61: A solution of NaOH in water is prepared by diluting a concentrated solution in an agitated, jacketed vessel. 2500 kg of 5 % NaOH solution is prepared by diluting 50 % NaOH solution. If the concentrated solution is available at 298 K and the solution discharged is also at 298 K, calculate the heat removed by the cooling water.
The heat of solution varies with concentration as:
| mol H2O/mol NaOH | 2 | 4 | 5 | 10 | ∞ |
| ∆Hs, kJ/mol NaOH | -22.9 | -34.4 | -37.7 | -42.5 | -42.9 |
Problem 12.62: Water at a rate of 54×103 kg/h and Cu(NO3)2.6H2O at a rate of 64.8×103 kg/h are mixed together in a tank. The solution is then passed through a heat exchanger to bring the temperature to 298 K, same as the components before mixing. Determine the rate of heat transfer in the exchanger. The following data are available. The heat of formation at 298 K of Cu(NO3)2 is –302.9 kJ and that of Cu(NO3)2·6H2O is −2110.8 kJ. The heat of solution of Cu(NO3)2⋅nH2O at 298 K is -47.84 kJ per kmol salt and is independent of n.
Problem 12.63: Hydrogen chloride gas at 373 K containing 10 % (weight) water vapor is absorbed in 25 % hydrochloric acid at 313 K yielding 28 % (weight) acid. The enthalpy of HCl gas at 373 K is 2065 J/kg and the enthalpy of the 25 % acid at 313 K is 163 J/kg. Calculate the enthalpy of the product.
Problem 12.64: If pure liquid H2SO4 is added to pure water both at 300 K to form a 20 percent (weight) solution, what is the final temperature of the solution? The heat of solution of sulphuric acid in water is H2SO4 (21.8 H2O) = −70×103 kJ/kmol of sulphuric acid. The standard heat of formation of water is 286 kJ/mol.
Problem 12.65: LiCl.H2O(c) is dissolved isothermally in enough water to form a solution containing 5 mol of water per mole of LiCl. What is the heat effect? The following enthalpies of formation are given: LiCl(c) = −409.05 kJ, LiCl·H2O(c) = −713.054 kJ, LiCl.(5H2O) = −437.232 kJ, H2O(l) = −286.03 kJ.
Problem 12.66: 1000 kg/h of FeSO4.7H2O crystals are to be produced in a Swenson-Walker crystallizer by cooling a saturated solution at 323 K (solubility is 140 parts FeSO4.7H2O per 100 parts water) to 300 K (solubility is 74 parts FeSO4·7H2O per 100 parts water). The feed solution has an average specific heat of 2.93 kJ/kg K. The heat of solution of FeSO4.7H2O at 300 K is -18 400 kJ/kmol. How much heat is evolved during the process?
Problem 12.67: Calculate the heat effects when 1.0 kmol of water is added to a solution containing 1.0 kmol sulphuric acid and 3.0 kmol of water. The process is isothermal and occurs at 298 K.
Data: Heat of mixing for H2SO4(3H2O) = −49 000 kJ per kmol H2SO4. Heat of mixing for H2SO4(4H2O) 54 100 kJ per kmol H2SO4.
Problem 12.68: A single-effect evaporator is used to concentrate a 15 percent (weight) solution of LiCl in water to 40 percent. The feed enters the evaporator at 298 K at the rate of 2 kg/s. The normal boiling point of a 40 percent LiCl solution is 405 K and its specific heat is 2.72 kJ/kg K. For what heat transfer rate in kJ/h, should the evaporator be designed?
The heat of solution of LiCl in water per mole of LiCl at 298 are:
∆Hs for LiCl (13.35 H2O) = −33.8 kJ, for LiCl (3.53 H2O) = −23.26 kJ, the enthalpy of superheated steam at 405 K = 2740.3 kJ/kg, the enthalpy of water at 298 K = 104.8 kJ/ kg, and the molecular weight of LiCl = 42.39.
Problem 12.69: A gas mixture consists of 60 % methane and 40 % nitrogen. Calculate the heating value of this mixture when it is metered at 300 K and 105 kPa if the partial pressure of water vapor in the gas is 4 kPa. The calorific value of methane gas is 40000 kJ/m3 measured at standard temperature and pressure.
Problem 12.70: Sulphur dioxide is circulated as the refrigerant in a small refrigerator. SO2 gas at a pressure of 5 bar and a temperature of 340 K is to be cooled at a constant volume of 0.142 m3, to 293 K as part of the refrigeration cycle. Calculate (a) The heat liberated (b) The work done by the gas on cooling (c) The final pressure attained on cooling (d) The change in enthalpy
Sulfur dioxide may be treated as an ideal gas. The specific heat (J/mol K) is found to vary with temperature (K) according to Cp = 25.736 + 5.796×10-2 T – 3.8112×10-5 T2 + 8.612×10-9 T3.
Problem 12.71: 10 kg of an equimolar mixture of CO and H2 at 1500 K and 1 bar is cooled at constant pressure to 350 K. Assuming that the gases are ideal determine the following: (a) The heat given off during cooling, (b) The change in internal energy, (c) The work done on the gas The specific heats in J/mol K are as follows:
C_{p,H_2}=29.086-8.3694\times10^{-4}T+2.0130\times10^{-6}T^2 C_{p,CO}=26.553+7.6882\times10^{-3}T-1.1727\times10^{-6}T^2Problem 12.72: One cubic meter of an ideal gas is confined in a cylinder provided with a frictionless piston at 300 K and 250 kPa. The gas is allowed to expand till its volume is doubled in a process occurring (a) at constant pressure and (b) at constant temperature. Calculate the work done by the gas on the piston in the above processes.
Problem 12.73: Consider 1 kg of water in a waterfall which is flowing down from a height of 100 m. At the bottom of the fall, it joins a river whose downstream velocity may be assumed negligible. Neglecting any energy exchange between the water and the surroundings, calculate (a) The potential energy at the top of the falls (b) The kinetic energy just before the water strikes the bottom (c) The change in temperature of the water when it enters the river.
Problem 12.74: A car riding downhill at a speed of 20 m/s was applied brake when it was at a height of 30 m vertically above the bottom of a hill. When the car comes to a halt at the bottom of the hill, how much energy as heat must be dissipated by the brakes, if wind and other frictional effects are neglected? The car weighed 1400 kg.
Problem 12.75: A system consisting of a gas confined in a cylinder undergoes the following series of processes before it is brought back to the initial conditions:
Step 1. A constant pressure process when it receives 50 J of work and gives up 25 J of heat.
Step 2. A constant volume process when it receives 75 J of heat.
Step 3. An adiabatic process.
Determine the change in internal energy during each step and the work done during the adiabatic process.
Problem 12.76: A 10-g lead ball at 300 K is dropped from a height of 10 m. Calculate (a) the kinetic energy and speed of the ball as it reaches the ground and (b) the temperature rises of the ball if all its kinetic energy is transformed into internal energy as the ball is suddenly stopped after 10 m, given that the specific heat of lead is 125.6 J/kg K and its volume change is negligible.
Problem 12.77: (a) Three kmol nitrogen gas (Cp = 29.1 kJ/kmol K and CV = 20.8 kJ/kmol K) at 350 K is taken in a rigid container and is heated to 550 K. How much heat must be supplied if the mass of the vessel is 100 kg and its specific heat is 0.5 kJ/kg K? (b) Two kmol nitrogen is taken in a piston/cylinder arrangement at 500 K. Determine the quantity of heat extracted from the gas to cool it to 350 K at constant pressure if the heat capacity of the container is negligible.
Problem 12.78: An insulated rigid container contains air at 5 bar and 375 K. The volume of the container is 1 m3. Air may be assumed to behave as an ideal gas. The specific heat CV of air is 20.785 kJ/kmol K. The temperature of the air is increased by a rotating paddle wheel. Calculate the work done to rise the temperature of the air to 425 K.
Problem 12.79: 100 m3 of CO2 initially at 423 K and 50 bar is to be isothermally compressed in a frictionless piston and cylinder device to a final pressure of 300 bar. Write a general expression for the energy balance for the gas within the piston and cylinder device as the system and define all terms. Also calculate the heat flow on compression.
Problem 12.80: A 14-m3 storage tank contains 13 m3 liquid oxygen in equilibrium with its vapor at 100 kPa. The tank is provided with a pressure relief valve which is set at 250 kPa. (a) Determine the mass of total material in the tank and (b) the fraction of the total material that is vapor. (c) When will the pressure relief valve operate if heat leaks into the tank at the rate of 5000 kJ/h? The specific volume of gas and liquid oxygen at 100 kPa are, respectively, 7.15 m3/kmol and 2.81×10-2 m3/kmol. The enthalpies are -133.5 kJ/kg and -116.6 kJ/kg at 100 kPa and 250 kPa respectively.
Problem 12.81: One kmole of an ideal gas is originally at 300 K and 1 bar. It is then heated at constant pressure to a temperature of 400 K and compressed isothermally to a volume equal to its initial volume. Assume that Cp = 30 kJ/kmol K. Find ∆U, ∆H, Q and W.
Problem 12.82: Argon gas at 300 K and 1.5 Pa contained in a chamber of volume 2×10-3 m3. A 1000-ohm electric resistance heater is used to heat the gas. The mass of the heater is 15 g and its heat capacity is 0.35 kJ/kg K. The gas may be assumed ideal with Cp = 5R/ 2. The heater draws current at 40 V for 5 minutes. Calculate the final gas temperature and pressure at equilibrium.
Problem 12.83: Hydrogenation of an edible oil is to be carried out in a reactor at a pressure of 136.8 kPa and a temperature of 453 K. The hydrogen gas at 293 K is heated to this temperature by passing through a coil where it experiences a pressure drop of 300 kPa. Hydrogen behaves like an ideal gas and its heat capacity at constant pressure is 29.4 kJ/kmol. Neglecting kinetic energy effects, determine the heat transfer rate in the coils per 1000 kg of hydrogen.
Problem 12.84: The heat capacities of nitrogen gas which is assumed as an ideal gas are CV = 20.8 and Cp = 29.1 kJ/kmol K. The gas initially at 10 bar and 280 K is undergoing a change of state to the final condition of 1 bar and 340 K. Determine the change in internal energy and the change in enthalpy.
Problem 12.85: One cubic meter of an ideal gas is being compressed adiabatically from an initial condition of 1 bar and 310 K to a pressure of 10 bar in an open system. If the efficiency of the process is 80 %, how much work is required? Take γ = 1.4. Compare the result with that if the operation is carried out in a closed system.
Problem 12.86: CO2 is sold commercially in steel containers at 60 bar. The gas is leaking through the outlet valve slowly so that the temperature may be assumed constant at the room temperature of 300 K. (a) What is the work done in the expansion of 10 kg of this gas from 60 bar to 1 bar? (b) If the temperature were constant at 290 K, would there be any difference in the work done? (c) What are the changes in enthalpy in both the above cases?
Problem 12.87: An ideal gas is compressed adiabatically from 1.5 bar, 338 K to 9 bar. The process is reversible, and γ = 1.23 is constant over the entire range of conditions. Calculate the following: (a) The temperature at the end of compression (b) The work of compression (c) The heat transferred (d) The change in internal energy (e) The change in enthalpy.
Problem 12.88: An ideal gas undergoes the following reversible processes: (a) From an initial state of 343 K and 1 bar, it is compressed adiabatically to 423 K. (b) It is then cooled to 343 K at constant pressure. (c) Finally, it is expanded to its original state isothermally.
Calculate ∆U, ∆H, W and Q for each step as well as for the entire cycle. Assume CV = (3/2)R.
Problem 12.89: Air initially at 389 K and 8 bar is expanded reversibly and isothermally to a pressure such that when it is cooled to 278 K at constant volume, its pressure is 2 bar. Assume air to be an ideal gas with Cp = 29.3 J/mol K. Calculate the work, heat transferred, changes in internal energy and change in enthalpy.
Problem 12.90: Assume that the P-V-T relationship for nitrogen gas can be approximated by the ideal gas equation PV = nRT, where R = 8.314 kJ/kmol K. The heat capacities are CV = 20.786 kJ/kmol K and Cp = 29.1 kJ/kmol K. Nitrogen which was initially at 1 bar and 280 K is compressed to 5 bar and 280 K by two different reversible processes: (a) Cooling at constant pressure followed by heating at constant volume (b) Heating at constant volume followed by cooling at constant pressure
For each of the above paths determine the conditions at the intermediate state and ∆U, ∆H, Q and W.
Problem 12.91: Methane is stored in a tank of capacity 5.7×10-2 m3 at a pressure of 15 bar and 294 K. The gas is allowed to flow from the tank through a partially opened valve to a gas holder where the pressure is constant at 1.15 bar. When the pressure in the tank dropped to 5 bar, what would be the mass of methane removed under the following conditions: (a) If the process took place slowly so that the temperature was constant. (b) If the process took place so rapidly that the heat transferred was negligible. Methane behaves as an ideal gas with γ = 1.4.
Problem 12.92: A rigid non-conducting tank with a volume of 4 m3 is divided into two equal parts by a membrane. On one side of the membrane the tank contained gas A at 5 bar and 350 K and on the other side a gas B at 10 bar and 450 K. A and B are ideal gases with CV values (5/2)R and (7/2)R respectively. The membrane is suddenly ruptured and the gases get mixed. What are the final temperature and pressure?
Problem 12.93: One cubic meter of an ideal gas at 600 K and 20 bar expands to ten times its initial volume as follows: (a) By a reversible, isothermal process (b) By a reversible, adiabatic process (c) By an irreversible, adiabatic process in which the expansion is against a restraining pressure of 1 bar
If Cp = 21 J/mol K, calculate the final temperature, pressure and the work done by the gas.
Problem 12.94: In a test of a water-jacketed air compressor, it was found that the shaft work required to drive the compressor was 150 kJ per kg air compressed. The enthalpy of air leaving the compressor was found to be greater than that of the air entering the compressor by 80 kJ/kg and the heat removed by the cooling water was 100 kJ per kg of air. Determine the amount of energy that must have been dissipated as heat to the atmosphere from the bearings, cylinder walls, etc.
Problem 12.95: A steam turbine using steam at 1368 kPa and 645 K and discharging saturated steam at 137 kPa is used to generate power for a certain chemical plant. The turbine acts adiabatically and the feed and discharge velocities may be considered equal. Determine the theoretical horsepower developed by the turbine if it uses 1650 kg of steam per hour. From steam tables, the enthalpy of superheated steam at 1368 kPa and 645 K = 3200 kJ/kg and the enthalpy of saturated steam at 137 kPa = 2690 kJ/kg.
Problem 12.96: 3600 kg/h of superheated steam at 200 kPa and 673 K enters a turbine with a velocity of 100 m/s. The inlet to the turbine is at an elevation of 10 m and the exit is at an elevation of 3 m. The steam leaves the turbine at a velocity of 150 m/s and is 98 % dry at a pressure of 10 kPa. What is the power output of the turbine if the energy loss from it is estimated to be 40000 kJ/h?
Problem 12.97: A trial run on a steam turbine power plant gave the following results
| Entrance to boiler: | Exit of turbine: |
| Mass flow rate = 3600 kg/h Enthalpy of water = 850 kJ/kg Elevation above datum = 4.3 m Velocity of water = 5 m/s | Velocity of steam = 25 m/s Elevation above datum = 0 Enthalpy of steam = 2625 kJ/kg |
Determine the power developed by the turbine if the heat added in the boiler is 2100 kJ/s.
Problem 12.98: In a small power plant steam at 573 K and 1800 kPa is expanded to 101.3 kPa with 85% quality at a rate of 0.1 kg/s. What is the horsepower developed by the turbine?
Problem 12.99: A turbine is fed with steam at 78 bar and 698 K (enthalpy = 3213 kJ/kg) at a rate of 1000 kg/h. Saturated steam at 5 bar (H = 2749 kJ/kg) is withdrawn from one point in the turbine at a rate of 250 kg/h. The remaining steam leaves the turbine saturated at 1 bar (H =2676 kJ/kg). Determine the power output from the turbine if it operates adiabatically.
Problem 12.100: A boiler receives water at 1800 kPa and 300 K where it is converted to superheated steam at 1800 kPa and 673K. The superheated steam is expanded in an adiabatic turbine and emerges at a pressure of 200 kPa and 98 % quality. Per kg of steam calculate the heat transferred, work done and the change in enthalpy for (a) the boiler and (b) the turbine.
Problem 12.101: Superheated steam at 2000 kPa and 873 K is expanded in a turbine at a rate of 100 kg/ min. The feed line is 75 mm in diameter and the turbine exhausts through a 125 mm diameter line after expanding adiabatically to 25 kPa. What is the horsepower rating of the turbine?
Problem 12.102: The work required for compressing gas from an initial condition of 100 kPa and 300 K to a final pressure of 300 kPa is found to be 280 kJ per kg of the gas. The compressed gas is admitted to a nozzle where its velocity is increased to 700 m/s. If the gas enters the compressor with negligible velocity and leaves the nozzle at 100 kPa and 300 K, what is the heat removed during compression?
Problem 12.103: Steam at 700 kPa and 553 K enters a nozzle with negligible velocity and discharges at a pressure of 475 kPa. Determine the following: (a) The exit velocity (b) The cross-sectional area at the nozzle exit for a flow rate of 0.5 kg/s.
Problem 12.104: Water at 368 K is pumped from a storage tank at the rate of 25 m3/h. The motor for the pump supplies work at the rate of 2 hp. The water passes through a heat exchanger, where it gives up heat at the rate of 42000 kJ/min and is delivered to a second storage tank at an elevation of 20 m above the first tank. What is the temperature of the water delivered to the second storage tank? Assume that the enthalpy of water is zero at 273 K and the specific heat of water is constant at 4.2 kJ/kg K.
Problem 12.105: Water is flowing in a straight horizontal insulated pipe 25 mm ID. There is no device present for adding or removing energy as work. The upstream velocity is 10 m/s. The water flows in a section where the diameter is suddenly increased. (a) What is the change in enthalpy if the downstream diameter is 50 mm? (b) What is the maximum enthalpy change for a sudden enlargement in the pipe?
Problem 12.106: Water at 293 K is being pumped from a constant head tank open to the atmosphere to a second tank kept at a constant pressure of 1150 kPa through a 50 mm ID pipe at a rate of 24 m3/h. The level of water in the second tank is 10 m above that in the first tank. The pump and motor have an overall efficiency of 70 %, and the energy loss in the pipeline is estimated to be 50 J/ kg. Determine the horsepower rating of the pump.
Problem 12.107: Water at 200 kPa and 355 K (H = 343.3 kJ/kg) enters a straight horizontal pipe at a velocity of 3 m/s, where it is heated by flue gases from the outside. Steam leaves the system at 100 kPa and 423 K (H = 2776.3 kJ/kg) at a velocity of 200 m/s. How much heat must have been supplied per kg of water flowing?
Problem 12.108: Calculate the horsepower rating of the pump required to pump 1000 kg/h of water from 600 kPa and 300 K to 6000 kPa and 310 K. The discharge is 5 m above the suction point.
Problem 12.109: Oil flows at a rate of 1000 kg/min from an open reservoir at the top of a hill, 400 m in height to another reservoir at the bottom of the hill. Heat is supplied to the oil on its way at the rate of 1800 kJ/min and work is supplied by a 1-hp pump. Take the mean specific heat of oil to be 3.35 kJ/kg K. Determine the temperature change of the oil.
Problem 12.110: A municipal water-supply system delivers water from a storage tank at a rate of 12 cubic meters per minute to consumers 15 m below the tank level utilizing pump work at a rate of 1.5 hp. If the exit velocity of water is 0.5 m/s and its temperature is the same as the temperature of water in the tank, estimate the heat loss from the system. Assume that the water level in the tank is essentially constant.
Problem 12.111: A pump is used to transfer a solution of density 1200 kg/m3 from a mixing vessel to a storage tank through a pipe of diameter 0.08 m at a velocity of 1 m/s. The level difference between the liquid in the mixing vessel and the storage tank is 20 m. Both tanks are open to the atmosphere. Frictional loss is estimated to be 300 W. Determine the pressure increase over the pump. What is the power input to the pump?
Problem 12.112: A pump is used to transfer a solution of density 1250 kg/m3 at a rate of 12 m3/h from an open storage tank to the top of an absorption tower, which is operated at a pressure of 500 kPa. The pump discharges into the tower through openings equivalent in area to a 25×10-3 m pipe. The point of discharge is 30 m above the level of solution in the tank. The pump intake is through a pipe of diameter 50×10-3 m which extends to a depth of 2 m below the level of solution in the tank. The friction head in the suction line is estimated to be 1.5 m of water and that in the discharge line is 10 m of water. If the efficiency of the pump is 70 %, what is the power input to the pump? What pressures will be indicated by the pressure gauges at the inlet and exit of the pump?
Problem 12.113: Air, assumed to be an ideal gas with molar heat capacity Cp = 30 kJ/kmol K, is flowing through a pipe of diameter 0.15 m at a rate of 0.3 m3/s at 100 kPa and 300 K before entering a compressor. A cooler removes heat from the compressed gas at a rate of 75.0 kJ/s. The gas at 315 K and 550 kPa is then carried away through a pipe of diameter 0.03 m. What is the power input to the compressor?
Problem 12.114: A solution of 10 % (weight) acetone in water is subjected to fractional distillation at a rate of 1000 kg/h to produce a distillate containing 99 % acetone and a bottom product containing not more than 100 ppm acetone. The feed enters at 308 K, and the distillate and residue leave the tower at 298 K and 373 K respectively. A reflux ratio (ratio of the weight of reflux to the weight of distillate product) of 10 is employed. The rise in temperature by 30 K is permitted for the cooling water circulated in the condenser employed for condensing the vapours into the distillate product and the reflux. Saturated steam at 276 kPa is available for supplying the heat of vaporization in the reboiler. Heat losses from the column may be neglected. The heat capacity of acetone is 2.2 kJ/kg K and that of water is 4.2 kJ/kg K. The boiling point of 99 % acetone-water solution is 330 K. The latent heat of acetone at 330 K is 620 kJ/kh and that of water is 2500 kJ/kg. The latent heat of steam at 276 kPa is 2730 kJ/kg. Calculate the following: (a) The cooling water circulation rate (b) The rate of circulation of steam.
Problem 12.115: Air at a rate of 100 kg/h enters a compressor at 100 kPa and 260 K with an enthalpy of 490 kJ/kg where it is compressed to 1000 kPa and 280 K. The air leaves the compressor at 65 m/s with an enthalpy 510 kJ/kg. Calculate the power required for the compressor.
Problem 12.116: Water flowing upward through a vertical pipe enters a reducer with a velocity of 1 m/s. The diameters at the entrance and exit of the reducer are 0.2 m and 0.1 m respectively. If the pressure at the entrance to the section is 105 kPa, what is the pressure at the exit given that the entrance and exit are 1.5 m apart?
Problem 12.117: 1000 kg/h of steam at 4500 kPa and 573 K enters the turbine through a 75 mm diameter main. In the turbine, steam expands at constant entropy (reversible adiabatic) to 10 kPa pressure. Determine (a) the power produced by the plant in kWh/day if the conversion of mechanical to electrical work is 90 % efficient and (b) the size of the exhaust main if the steam were to have the same velocity as in the inlet main.
Problem 12.118: The feed to a distillation column consists of 10000 kg/h of a mixture of benzene and toluene containing 45 % (mole) benzene at 300 K. On fractionation of this mixture a distillate containing 99 % (mole) benzene and a residue consisting of 1.5 % (mole) benzene are obtained. The distillate is condensed at 355 K and further cooled to 350 K in the overhead condenser. The residue leaves at 383 K. A reflux ratio of 8 is employed. Saturated steam at 412 K (λ = 2148 kJ/kg) is supplied to the reboiler. The vapor produced in the reboiler is 3.5% (mole) benzene. The temperature rise for cooling water is limited to 30 K. The latent heat of condensation of the distillate vapor is 32.05 kJ/mol. The heat capacity of all liquid streams in the column may be assumed to be 160 kJ/kmol K. Calculate the rate of circulation of cooling water and the steam supply rate in kg/h.
Problem 12.119: A steam heated dryer evaporates 1000 kg/h of water from a wet solid material. The dryer is operated at atmospheric pressure. Air enters the dryer at 303 K and 293 K wet bulb and leaves at 365 K containing 0.3 mol water per mol dry air. The solid enters the dryer at 290 K and the enthalpy change in the solid may be neglected. The heat loss from the dryer is estimated to be 5 % of the total heat duty of the dryer. Calculate the heat duty of the dryer.
Problem 12.120: A steam-jacketed vessel is charged with 200 kg of a feed material (heat capacity 3.5 kJ/kg K) at 295 K to heat it to 373 K. The heating is done by complete condensation of saturated steam at 40 bar (λ = 1714 kJ/kg) in the jacket. The rate of heat loss from the vessel is estimated to be at a rate of 1.5 kJ/s. Determine the mass of steam needed if the charge was heated for one hour.
Problem 12.121: 10000 kg/h of a wet solid containing 5 % water on a wet basis is to be dried to 0.10 % in a counter-current rotary drier. The feed enters the drier at 300 K. Drying air enters the drier at 422 K and leaves at 343 K. The solid leaves the drier at 366 K. The heat capacity of the solid may be taken as 1.5 kJ/kg K. The evaporation of the moisture occurs at 307 K. The latent heat of vaporization of water at 307 K is 2420 kJ/kg and the specific heat of water vapor is 1.884 kJ/kg K. Calculate the following: (a) The amount of heat required to bring the product to the discharge temperature (b) The amount of heat required to remove the moisture in the solid.
Problem 12.122: Saturated steam at 500 K circulated at a rate of 100 kg/h is used as the heating medium for preheating the feed to a reactor. Determine the amount of heat transferred to the feed stream in one hour if the condensate leaving is at 425 K. If subcooling is not allowed in the condenser, how much additional steam is to be supplied for the same heat duty?
Problem 12.123: A liquid mixture consisting of 30 % (mole) ethane and the rest n-butane at 280 K and very high pressure is first heated by passing through a heat exchanger and then throttled to a lower pressure of 1400 kPa. On throttling, partial vaporization of the mixture takes place. The mixture is admitted into a flash chamber maintained at 1400 kPa. The vapor and liquid products are separated here at 328 K. The vapor product contains 60 % (mol) ethane and the liquid product contains 17 % (mol) ethane. The enthalpy values are: feed at 280 K = -8500 kJ/kmol, vapour at 328 K = 14 000 kJ/ kmol and liquid at 328 K = -3500 kJ/kg. Find the quantity of heat required for the flash vaporization of 100 kmol of the feed.
Problem 12.124: The discharge air from a drier has a dry-bulb temperature of 330 K and a wet-bulb temperature of 317 K (humidity = 0.06 kg of water per kg of dry air, enthalpy 228 kJ/ kg dry air). To keep the drying rate within limits and to avoid undesirable effects, a portion of this air is recycled and is mixed with fresh air before being sent to the heater and then to the drier. Eighty percent of the dry air entering the heater is recycled. Fresh air supplied is at 249 K with humidity 0.006 kg of water per kg of dry air (enthalpy of fresh air is 49 kJ/kg). How much heat is required per kilogram of water evaporated?
Problem 12.125: Ammonium sulfate is dried from 3.5 % moisture to 0.2 % moisture in a counter-current rotary drier at a rate of 1000 kg/h of product. Atmospheric air at 298 K, 50 % humidity will be heated by passage over steam coils to 363 K before it is admitted into the drier. The air leaves the drier at 305 K. The solids enter the drier at 298 K and is expected to be discharged at 333 K. The heat loss from the drier is 40×103 kJ/h. Determine the following: (a) The air circulation rate, kg/h (b) The heat duty of the drier, kJ/h
The heat capacity of ammonium sulfate is 1.5 kJ/kg K, the heat capacity of dry air is 1.005 kJ/kg K, the specific heat of water vapor is 1.884 kJ/kg k and the latent heat of vaporization of water at 273 K is 2502 kJ/kg.
Problem 12.126: Air, with a dry-bulb temperature 311 K and wet-bulb temperature 300 K, is scrubbed with water to remove dust. The water is maintained at 298 K. The air leaving the scrubber is in equilibrium with water. It is then heated to 366 K in an air pre-heater and admitted to an adiabatic rotary drier. The air leaves the drier 322 K. The material to be dried enters and leaves the drier at 319 K. The material loses moisture at a rate of 0.05 kg of water per kg of product The total product is 1000 kg/h. Using the psychrometric chart, determine the heat supplied to the air pre-heater in kJ/h.