GATE-CH-1994-4-o-td-1mark

Match the following:

• I. dH

Answer 1B. TdS + VdPA. TdS - PdVD. VdP - SdTC. -PdV - SdT

• II. dG

Answer 2B. TdS + VdPA. TdS - PdVD. VdP - SdTC. -PdV - SdT

GATE-CH-1989-6-ii-b-td-1mark

Entropy is :

• Intensive property

• Derived property

• Extensive property

• None of the above

GATE-CH-1991-7-iv-td-2mark

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:

• the volume of the liquid phase is negligible compared to that of the vapor phase

• the vapor phase behaves as an ideal gas

• the heat of vaporization is independent of temperature

• all of the above are applicable

GATE-CH-1993-5-e-td-1mark

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

• \(\delta Q = dU + \delta W\)

• \(T dS = dU + \delta W\)

• \(T dS = dU + P dV\)

• \(\delta Q = P dV + dU\)

GATE-CH-1996-1-20-td-1mark

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

• an open system of constant composition

• a closed system of constant composition

• an open system with changes in composition

• a closed system with changes in composition

GATE-CH-1997-1-20-td-1mark

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

• positive

• negative

• zero

• may be positive or negative

GATE-CH-2001-2-4-td-2mark

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

• \((\partial T/\partial V)_S = -(\partial P/\partial S)_V\)

• \((\partial S/\partial P)_T = -(\partial V/\partial T)_P\)

• \((\partial V/\partial S)_P = (\partial T/\partial P)_S\)

• \((\partial S/\partial V)_T = (\partial P/\partial T)_V\)

GATE-CH-2001-2-5-td-2mark

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:

• significantly less than 4.69 atm

• nearly equal to 4.69 atm

• significantly more than 4.69 atm

• indeterminate due to lack of data

GATE-CH-2002-1-23-td-1mark

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

• \((\partial T/\partial V)_S=-(\partial P/\partial S)_V\)

• \((\partial T/\partial P)_S=(\partial V/\partial S)_P\)

• \((\partial P/\partial T)_V=(\partial S/\partial V)_T\)

• \((\partial V/\partial T)_P=-(\partial S/\partial P)_T\)

GATE-CH-2007-31-td-2mark

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

• \((\partial T/\partial V)_S = -(\partial P/\partial S)_V\)

• \((\partial P/\partial T)_V = -(\partial S/\partial V)_T\)

• \((\partial T/\partial P)_S = -(\partial V/\partial S)_P\)

• \((\partial V/\partial T)_P = -(\partial S/\partial P)_T\)

GATE-CH-2009-6-td-1mark

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?

• \(U_1=U_2, G_1>G_2\)

• \(U_1=U_2, G_1<G_2\)

• \(U_1>U_2, G_1=G_2\)

• \(U_1<U_2, G_1=G_2\)

GATE-CH-2012-7-td-1mark

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

• Liquid

• Liquid-vapor coexistence

• Saturated vapor

• Solid

GATE-CH-2015-7-td-1mark

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.)

• \(\Delta U, \Delta S, Q\) are the same

• \(W, \Delta U, \Delta G\) are the same

• \(\Delta S, W, Q\) are the same

• \(\Delta G, \Delta U, \Delta S\) are the same

GATE-CH-2015-9-td-1mark

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.

Group-1		Group-2
P.	\(-(\partial U/\partial V)_S\)	I.	Temperature
Q.	\((\partial G/\partial P)_T\)	II.	Pressure
R.	\(-(\partial G/\partial T)_P\)	III.	\(V\)
S.	\((\partial U/\partial S)_V\)	IV.	\(S\)

• P-II, Q-III, R-IV, S-1

• P-II, Q-IV, R-III, S-I

• P-I, Q-IV, R-II, S-III

• P-III, Q-II, R-IV, S-I

GATE-XE-2009-E-7-td-1mark

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

• less than that of constant pressure line

• more than that of constant pressure line

• less than that of constant enthalpy line

• equal to that of constant enthalpy line

GATE-XE-2014-E-7-td-1mark

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

• \(\displaystyle dU = C_PdT + \left (\frac {\partial U}{\partial V}\right )_T dV\)

• \(\displaystyle dU = C_PdT + \left (\frac {\partial U}{\partial P}\right )_T dP\)

• \(\displaystyle dU = C_VdT + \left (\frac {\partial U}{\partial V}\right )_T dV\)

• \(\displaystyle dU = C_VdT\)

GATE-CH-2015-6-td-1mark

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) ____________

• Answer

GATE-CH-2003-48-49-td-4mark

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.

(i) The amount of water vapor condensed (in kg) is

{#1}

(ii) The latent heat of condensation (kJ/kg) under these conditions is

{#2}

GATE-CH-2004-47-td-2mark

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

• 0.07

• 0.09

• 0.11

• 0.13

GATE-CH-2007-33-td-2mark

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?

Data:
\(T=175\)^oC, \(P = 400\) kPa, \(V=0.503\) m³/kg, \(U=2606\) kJ/kg, \(S = 7.055\) kJ/(kg.K)
\(T=175\)^oC, saturated vapor, \(V=0.216\) m³/kg, \(U=2579\) kJ/kg, \(S = 6.622\) kJ/(kg.K)

• 0 kJ

• 230 kJ

• 334 kJ

• 388 kJ

GATE-CH-2014-35-td-2mark

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

• \(\displaystyle \left ( \frac {\partial U}{\partial V} \right )_S V = R \left ( \frac {\partial U}{\partial S} \right )_V \)

• \(\displaystyle -\left ( \frac {\partial H}{\partial P} \right )_S P = R \left ( \frac {\partial H}{\partial S} \right )_P \)
  
  

• \(\displaystyle \left ( \frac {\partial U}{\partial V} \right )_S V = R \left ( \frac {\partial H}{\partial S} \right )_P \)

• \(\displaystyle \left ( \frac {\partial H}{\partial P} \right )_S P = R \left ( \frac {\partial U}{\partial S} \right )_V \)

GATE-CH-1996-27-td-5mark

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 \((P + 365/V^2)(V - 0.043) = RT\).

• Answer

GATE-CH-2016-33-td-2mark

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 ____________

• Answer

GATE-CH-2017-32-td-2mark

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.

• Answer

GATE-CH-0200-2-td-5mark

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

1. \(\displaystyle \left(\frac{\partial P}{\partial T}\right)_V\)

2. \(\displaystyle \left(\frac{\partial^2 P}{\partial T^2}\right)_V\)

3. \(\displaystyle \left(\frac{\partial V}{\partial P}\right)_T\)

• Answer