# Thermodynamics GATE-2015

**Q 1.** Three identical closed systems of a pure gas are taken from an initial temperature and pressure (T_{1}, P_{1}) to a final state (T_{2}, P_{2}), each by different path. Which of the following is ALWAYS TRUE for the three systems? (Δ represents the change between the initial and final states; U, S, G, Q and W are internal energy, entropy, Gibbs free energy, heat added and work done respectively)

**Q 2.** For a gas phase cracking reaction, A\rightarrow B+C at 300^{0} C, the Gibbs free energy of the reaction at this temperature is ΔG^{o} = −2750 J/mol. The pressure is 1 bar and the gas phase can be assumed to be ideal. The universal gas constant R = 8.314 J/mol.K. The fractional molar conversion of A at equilibrium is:

**Q 3.** If v, u, s and g represent respectively the molar volume, molar internal energy, molar entropy, and molar Gibbs free energy, then math the entries in the left and right columns below and choose the correct option.

P. -{\left(\frac{\partial u}{\partial v}\right)}_s | I. Temperature |

Q. {\left(\frac{\partial g}{\partial P}\right)}_T | II. Pressure |

R. -{\left(\frac{\partial g}{\partial T}\right)}_P | III. v |

S. {\left(\frac{\partial u}{\partial s}\right)}_v | IV. s |

**Q 4.** An ideal gas is initially at a pressure of 0.1 MPa and a total volume of 2 m^{3}. It is first compressed to 1 MPa by a reversible adiabatic process and then cooled at constant pressure to a final volume of 0.2 m^{3}. The total work done (in kJ) on the gas for the entire process (up to one decimal place) is _____________.

Data: R = 8.314 J/mol.K; heat Capacity at constant pressure (C_{P}) = 2.5R

**Q 5.** Given that molar residual Gibbs free energy, g^{R}, and molar residual volume, v^{R}, are related as \frac{g^R}{RT}=\int_0^P\left(\frac{v^R}{RT}\right)dP , find g^{R} at T = 27^{o} C and P = 0.2 MPa. The gas may be assumed to follow the virial equation of state, z = 1 + BP/RT, where B = −10^{-4} m^{3}/mol at the given conditions (R = 8.314 J/mol.K) the value of g^{R} in J/mol is:

**Q 6.** A binary mixture of components (1) and (2) forms an azeotrope at 130^{o} C and x_{1} = 0.3. The liquid phase non-ideality is described by ln γ_{1} = Ax_{2}^{2} and ln γ_{2} = Ax_{1}^{2}, where γ_{1}, γ_{2} are the activity coefficients, and x_{1}, x_{2} are the liquid phase mole fractions. For both components, the fugacity coefficients are 0.9 at the azeotropic composition. Saturated vapor pressures at 130^{o} C are P_{1}^{sat} = 70 bar and P_{2}^{sat} = 30 bar.

The total pressure in bars for the above azeotropic system (up to two decimal places) is ___________.