Thermodynamics - GATE-CH Questions

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Solution Thermodynamics

GATE-CH-1996-2-9-td-2mark

1996-2-9-td

The theoretical minimum work required to separate one mole of a liquid mixture at 1 atm, containing 50 mole % each of n-heptane and n-octane into pure compounds each at 1 atm is

GATE-CH-2002-1-22-td-1mark

2002-1-22-td

The partial molar enthalpy of a component in an ideal binary gas mixture of composition \(z\), at a temperature \(T\) and pressure \(P\), is a function only of

GATE-CH-2003-6-td-1mark

2003-6-td

When dilute aqueous solutions of two salts are mixed, the process is associated with

GATE-CH-2004-8-td-1mark

2004-8-td

As pressure approaches zero, the ratio of fugacity to pressure (\(f/P\)) for a gas approaches

GATE-CH-2007-9-td-1mark

2007-9-td

If \(m_i, \overline {m}_i, m_i^R, m_i^E\) are molar, partial molar, residual and excess properties respectively for a pure species “\(i\)”, the mixture property \(M\) of a binary non-ideal mixture of components 1 and 2, is given by


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GATE-CH-2011-13-td-1mark

2011-13-td

The partial molar enthalpies of mixing (in J/mol) for benzene (component 1) and cyclohexane (component 2) at 300 K and 1 bar are given by \(\Delta \bar {H_1} = 3600 x_2^2\) and \(\Delta \bar {H_2}=3600 x_1^2\), where \(x_1\) and \(x_2\) are the mole fractions. When one mole of benzene is added to two moles of cyclohexane, the enthalpy change (in J) is

GATE-CH-2011-9-td-1mark

2011-9-td

Minimum work \((W)\) required to separate a binary gas mixture at a temperature \(T_0\) and pressure \(P_0\) is \[ W = -RT_0 \left [ y_1\ln \left (\frac {\hat {f_1}}{f_{\text {pure,1}}}\right ) + y_2 \ln \left (\frac {\hat {f_2}}{f_{\text {pure,2}}}\right ) \right ] \] where \(y_1\) and \(y_2\) are mole fractions, \(f_{\text {pure,1}}\) and \(f_{\text {pure,2}}\) are fugacities of pure species at \(T_0\) and \(P_0\), and \(\hat {f_1}\) and \(\hat {f_2}\) are fugacities of species in the mixture at \(T_0, P_0\) and \(y_1\). If the mixture is ideal then \(W\) is

GATE-CH-1993-6-7-td-1mark

1993-6-7-td

A rigid insulated cylinder has two compartments separated by a thin membrane. While one compartment contains 1 kmol nitrogen at a certain temperature and pressure, the other contains 1 kmol of \(\ce {CO2}\) at the same temperature and pressure. The membrane is ruptured and the two gases are allowed to mix. Assume that the gases behave as ideal gases. Calculate the increase in entropy (J/K) of the contents of the cylinder. Universal gas constant \(R = 8314\) J/kmol.K

GATE-CH-2016-5-td-1mark

2016-5-td

The partial molar enthalpy (in kJ/mol) of species 1 in a binary mixture is given by \(\bar {H}_1=2-60x_2^2+100x_1x_2^2\), where \(x_1\) and \(x_2\) are the mole fractions of species 1 and 2, respectively. The partial molar enthalpy (in kJ/mol, rounded off to the first decimal place) of species 1 at infinite dilution is ____________

GATE-CH-2008-35-td-2mark

2008-35-td

The molar volume (\(V\)) of a binary mixture, of species 1 and 2 having mole fractions \(x_1\) and \(x_2\) respectively is given by \[ V = 220 x_1 + 180 x_2 + x_1x_2(90x_1+50x_2) \] The partial molar volume of species 2 at \(x_2=0.3\) is


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GATE-CH-2010-31-td-2mark

2010-31-td

At constant \(T\) and \(P\), the molar density of binary mixture is given by \(\rho =1+x_2\), where \(x_2\) is the mole fraction of component 2. The partial molar volume at infinite dilution for component 1, \(\bar {V_1}^\infty \), is

GATE-CH-2012-31-td-2mark

2012-31-td

Consider a binary liquid mixture at constant temperature \(T\) and pressure \(P\). If the enthalpy change of mixing, \(\Delta H = 5 x_1 x_2\), where \(x_1\) and \(x_2\) are the mole fraction of species 1 and 2 respectively, and the entropy change of mixing \(\Delta S = -R[x_1\ln x_1 + x_2 \ln x_2]\) (with \(R=8.314\) J/mol.K), then the minimum value of the Gibbs free energy change of mixing at 300 K occurs when

GATE-CH-2015-32-td-2mark

2015-32-td

Given that molar residual Gibbs free energy, \(G^{\text {R}}\), and molar residual volume, \(V^{\text {R}}\), are related as \(\displaystyle \frac {G^{\text {R}}}{RT} = \int _0^P\left (\frac {V^{\text {R}}}{RT}\right )dP\), find \(G^{\text {R}}\) at \(T=27\)oC  and \(P=0.2\) MPa. The gas may be assumed to follow the virial equation of state, \(Z=1+BP/RT\), where \(B=-10^{-4}\) m3/mol at the given conditions. (\(R=8.314\) J/mol.K). The value of \(G^{\text {R}}\) in J/mol is:

GATE-CH-2013-31-td-2mark

2013-31-td

A binary liquid mixture is in equilibrium with its vapor at a temperature \(T = 300\) K. The liquid mole fraction \(x_1\) of species 1 is 0.4 and the molar excess Gibbs free energy is 200 J/mol. The value of the universal gas constant is 8.314 J/mol.K, and \(\gamma _i\) denotes the liquid-phase activity coefficient of species \(i\). If \(\ln (\gamma _1) = 0.09\), then the value of \(\ln (\gamma _2)\), up to 2 digits after the decimal point, is ____________

GATE-CH-2016-34-td-2mark

2016-34-td

A binary system at a constant pressure with species `1' and '2' is described by the two-suffix Margules equation, \(\displaystyle \frac {G^E}{RT}=3x_1x_2\), where \(G^E\) is the molar excess Gibbs free energy, \(R\) is the universal gas constant, \(T\) is the temperature and \(x_1\), \(x_2\) are the mole fractions of species 1 and 2, respectively. At a temperature \(T\), \(\dfrac {G_1}{RT} = 1\) and \(\dfrac {G_2}{RT} = 2\), where \(G_1\) and \(G_2\) are the molar Gibbs free energies of pure species 1 and 2, respectively. At the same temperature, \(G\) represents the molar Gibbs free energy of the mixture. For a binary mixture with 40 mole% of species 1, the value (rounded off to the second decimal place) of \(\dfrac {G}{RT}\) is ____________


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GATE-CH-2017-34-td-2mark

2017-34-td

The vapor pressure of a pure substance at a temperature \(T\) is 30 bar. The actual and ideal gas values of \(G/RT\) for the saturated vapor at this temperature \(T\) and 30 bar are 7.0 and 7.7, respectively. Here, \(G\) is the molar Gibbs free energy and \(R\) is the universal gas constant. The fugacity of the saturated liquid at these conditions, rounded to 1 decimal place, is ____________bar.

GATE-CH-2019-38-td-2mark

2019-38-td

For a given binary system at constant temperature and pressure, the molar volume (in m3/mol) is given by: \(V=30x_A+20x_B+x_Ax_B(15x_A-7x_B)\), where \(x_A\) and \(x_B\) are the mole fractions of components \(A\) and \(B\), respectively. The volume change of mixing \(\Delta V_{\text {mix}}\) (in m3/mol) at \(x_A=0.5\) is ____________

GATE-CH-1988-16-ii-td-6mark

1988-16-ii-td

At 30\(^\circ \)C and 1 atm, the volumetric data for a liquid mixture of benzene(\(1\)) and cyclo-benzene(\(2\)) are represented by the equation \[ V (\text { cm\(^3\)/gmol}) = 109.4 - 16.8x_1 - 2.64x_1^2 \] where \(x_1\) is the mole fraction of benzene. Find an expression for the partial molar volumes of the two components \(\bar {V}_1\) and \(\bar {V}_2\).

GATE-CH-1990-6-i-td-2mark

1990-6-i-td

Isothermal mixing of pure gases always produces a decrease in the --------------- . Hence work has to be done --------------- the system for separating a mixture of gases into its components.


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Last Modified on: 04-May-2024

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