Match the following:

Entropy is :

To obtain the integrated form of Clausius-Clapeyron equation \[ \ln \frac {P_2}{P_1} = \frac {\Delta H_V}{R}\left (\frac {1}{T_1} - \frac {1}{T_2} \right ) \] from the exact Clapeyron equation, it is assumed that:

Which among the following relations is/are valid ONLY for reversible process undergone by a pure substance?

The equation \(dU = TdS - PdV\) is applicable to infinitesimal changes occurring in

The change in Gibbs free energy for vaporization of a pure substance is

The Maxwell relation derived from the differential expression for the Helmholtz free energy (\(dA\)) is:

At 100^oC , water and methylcyclohexane both have vapor pressures of 1.0 atm. Also at 100^oC , the latent heats of vaporization of these compounds are 40.63 kJ/mol for water and 31.55 kJ/mol for methylcyclohexane. The vapor pressure of water at 150^oC is 4.69 atm. At 150^oC , the vapor pressure of methylcyclohexane would be expected to be:

Which of the following identities can be most easily used to verify steam table data for superheated steam?

For a pure substance, the Maxwell’s relation obtained from the fundamental property relation \(dU = TdS - PdV\) is

An ideal gas at temperature \(T_1\) and pressure \(P_1\) is compressed isothermally to pressure \(P_2(>P_1)\) in a closed system. Which ONE of the following is TRUE for internal energy (\(U\)) and the Gibbs free energy (\(G\)) of the gas at the two states?

If the temperature of saturated water is increased infinitesimally at constant entropy, the resulting state of water will be

Three identical closed systems of pure gas are taken from an initial temperature and pressure (\(T_1,P_1\)) to a final state (\(T_2,P_2\)), each by a different path. Which of the following is ALWAYS TRUE for the three systems? (\(\Delta \) 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.)

If \(V,U,S\) and \(G\) represent respectively the molar volume, molar internal energy, molar entropy and molar Gibbs free energy, then match the entries in the Group-1 and Group-2 below and choose the correct option.

On a \(T\)-\(S\) diagram, the slope of the constant volume line for an ideal gas is

For a superheated vapor that cannot be approximated as an ideal gas, the expression determining a small change in the specific internal energy is

For a pure liquid, the rate of change of vapor pressure with temperature is 0.1 bar/K in the temperature range of 300 to 350 K. If the boiling point of the liquid at 2 bar is 320 K, the temperature (in K) at which it will boil at 1 bar (up to one decimal place is) ____________

One kg of saturated steam at 100^oC and 1.01325 bar is contained in a rigid walled vessel. It has a volume of 1.673 m³. It cools to 98^oC; the saturation pressure is 0.943 bar; one kg of water vapor under these conditions has a volume of 1.789 m³.

The vapor pressure of water is given by \(\displaystyle \ln P^{\text {sat}} = A - \frac {5000}{T}\), where \(A\) is a constant, \(P^{\text {sat}}\) is vapor pressure in atm, and \(T\) is temperature in K. The vapor pressure of water in atm at 50^oC is approximately

2 kg of steam in a piston-cylinder device at 400 kPa and 175^oC undergoes a mechanically reversible, isothermal compression to a final pressure such that the steam becomes just saturated. What is the work, \(W\) required for the process?

Which ONE of the following is CORRECT for an ideal gas in a closed system?

Calculate the change in internal energy (in J) of 25 kmol of \(\ce {CO2}\) gas when it is isothermally expanded from 10132 kPa to 101.32 kPa at 373 K, the corresponding molar volumes being 0.215 m\(^3\)/kmol and 30.53 m\(^3\)/kmol. Assume \(\ce {CO2}\) to obey \((P + 365/V^2)(V - 0.043) = RT\).

A gas obeying the Clausius equation of state is isothermally compressed from 5 MPa to 15 MPa in a closed system at 400 K. The Clausius equation of state is \(\displaystyle P= \frac {RT}{V-b}\) where \(P\) is the pressure, \(T\) is the temperature, \(V\) is the molar volume and \(R\) is the universal gas constant. The parameter \(b\) in the above equation varies with temperature as \(b(T)=b_0+b_1T\) with \(b_0=4\times 10^{-5}\) m³.mol^-1and \(b_1=1.35\times 10^{-7}\) m³.mol^-1.K^-1. The effect of pressure on the molar enthalpy (\(H\)) at a constant temperature is given by \(\displaystyle \left (\frac {\partial H}{\partial P} \right )_T=V-T\left (\frac {\partial V}{\partial T} \right )_P\). Let \(H_i\) and \(H_f\) denote the initial and final molar enthalpies, respectively. The change in the molar enthalpy \(H_f-H_i\) (in J.mol\(^{-1}\), rounded off to the first decimal place) for this process is ____________

The pressure of a liquid is increased isothermally. The molar volume of the liquid decreases from \(50.45\times 10^{-6}\) m³/mol to \(48\times 10^{-6}\) m³/mol during this process. The isothermal compressibility of the liquid is \(10^{-9}\) Pa^-1, which can be assumed to be independent of pressure. The change in molar Gibbs free energy of the liquid, rounded to nearest integer, is ____________J/mol.

For 1 mole of a van der Waals gas, evaluate the following coefficients: