Thermodynamic Potentials and Property Relations - Thermodynamic Relations - Engineering Sciences Previous Year Questions

1

2007 · Engineering Sciences · Thermodynamic Relations · Thermodynamic Potentials and Property Relations

Engineering Sciences (XE) 2007

In the following T-p diagram, an inversion curve is shown. Which one of the following is correct?

A

Region 1: Cooling, Region 2: Cooling

B

Region 1: Heating, Region 2: Cooling

C

Region 1: Cooling, Region 2: Heating

D

Region 1: Heating, Region 2: Heating

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2

2007 · Engineering Sciences · Thermodynamic Relations · Thermodynamic Potentials and Property Relations

Engineering Sciences (XE) 2007

For a system containing an ideal gas, the difference between Gibbs function and Helmholtz function

A

depends on pressure only

B

depends on temperature only

C

depends on both pressure and temperature

D

is independent of both pressure and temperature

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3

2008 · Engineering Sciences · Thermodynamic Relations · Thermodynamic Potentials and Property Relations

Engineering Sciences (XE) 2008

Which one of the following relations is wrong?

A

\(\left(\frac{\partial T}{\partial v}\right)_s = -\left(\frac{\partial P}{\partial s}\right)_v\)

B

\(\left(\frac{\partial T}{\partial P}\right)_s = \left(\frac{\partial v}{\partial s}\right)_P\)

C

\(\left(\frac{\partial P}{\partial T}\right)_v = \left(\frac{\partial s}{\partial v}\right)_T\)

D

\(\left(\frac{\partial s}{\partial P}\right)_T = -\left(\frac{\partial v}{\partial T}\right)_P\)

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4

2008 · Engineering Sciences · Thermodynamic Relations · Thermodynamic Potentials and Property Relations

Engineering Sciences (XE) 2008

Carbon tetrachloride boils at 76 °C at 101 kPa. The latent heat of vaporization of carbon tetrachloride is 195 kJ/kg and for this, the characteristic gas constant is 0.055 kJ/kg·K. The boiling point of carbon tetrachloride at 202 kPa is

A

274.54 K

B

374.54 K

C

474.54 K

D

574.54 K

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5

2008 · Engineering Sciences · Thermodynamic Relations · Thermodynamic Potentials and Property Relations

Engineering Sciences (XE) 2008

The quality of the steam at the outlet of the device is

A

0.548

B

0.648

C

0.748

D

0.948

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6

2009 · Engineering Sciences · Thermodynamic Relations · Thermodynamic Potentials and Property Relations

Engineering Sciences (XE) 2009

Air (\( \gamma = 1.4 \)) is compressed ideally from an initial state of 1 bar, 300 K to a final temperature of 600 K. The value of the final pressure in bar is

A

2

B

3.7

C

7.2

D

11.3

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7

2010 · Engineering Sciences · Thermodynamic Relations · Thermodynamic Potentials and Property Relations

Engineering Sciences (XE) 2010

\(\left(\frac{\partial P}{\partial T}\right)_S\) is equal to

A

\(\left(\frac{\partial S}{\partial V}\right)_P\)

B

\(-\left(\frac{\partial S}{\partial V}\right)_P\)

C

\(\left(\frac{\partial S}{\partial V}\right)_T\)

D

\(-\left(\frac{\partial S}{\partial V}\right)_T\)

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8

2011 · Engineering Sciences · Thermodynamic Relations · Thermodynamic Potentials and Property Relations

Engineering Sciences (XE) 2011

Which one of the following expressions represents the Joule-Thomson coefficient?

A

\(\left(\frac{\partial T}{\partial p}\right)_h\)

B

\(\left(\frac{\partial T}{\partial v}\right)_h\)

C

\(\left(\frac{\partial p}{\partial h}\right)_s\)

D

\(\left(\frac{\partial s}{\partial T}\right)_p\)

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9

2012 · Engineering Sciences · Thermodynamic Relations · Thermodynamic Potentials and Property Relations

Engineering Sciences (XE) 2012

The slope of a Mollier diagram at constant pressure indicates

A

enthalpy

B

entropy

C

internal energy

D

temperature

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10

2012 · Engineering Sciences · Thermodynamic Relations · Thermodynamic Potentials and Property Relations

Engineering Sciences (XE) 2012

Joule-Thomson coefficient for a gas, \(\mu_J\), obeying the relation \(p(v-b)=RT\) is

A

\(\mu_J = \frac{c_p}{b}\)

B

\(\mu_J = \frac{b}{c_p}\)

C

\(\mu_J = -\frac{b}{c_p}\)

D

\(\mu_J = -\frac{c_p}{b}\)

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11

2012 · Engineering Sciences · Thermodynamic Relations · Thermodynamic Potentials and Property Relations

Engineering Sciences (XE) 2012

The correct expression representing \(Z\) to be a thermodynamic property is

A

\(Z = pdv\)

B

\(Z = vdp\)

C

\(Z = pdv + vdp\)

D

\(Z = pdv - vdp\)

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12

2013 · Engineering Sciences · Thermodynamic Relations · Thermodynamic Potentials and Property Relations

Engineering Sciences (XE) 2013

Which of the following processes, shown in the figure below, represents the throttling of an ideal gas?

A

1 to 2

B

1 to 3

C

1 to 4

D

1 to 5

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13

2013 · Engineering Sciences · Thermodynamic Relations · Thermodynamic Potentials and Property Relations

Engineering Sciences (XE) 2013

On a ln pvs h coordinate system, where ln p is the y-coordinate and h is the x coordinate, the slope of a constant entropy line is

A

1/v

B

v

C

p/v

D

1/(pv)

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14

2013 · Engineering Sciences · Thermodynamic Relations · Thermodynamic Potentials and Property Relations

Engineering Sciences (XE) 2013

Starting from the definition of Gibbs free energy function g=h-Ts, the Maxwell relation that can be derived is

A

\(\left(\frac{\partial p}{\partial T}\right)_{s}=\frac{v}{s}\)

B

\(\left(\frac{\partial p}{\partial T}\right)_{s}=v\)

C

\(\left(\frac{\partial v}{\partial s}\right)_{T}=-\frac{\partial p}{\partial T}_{s}\)

D

\(\left(\frac{\partial v}{\partial T}\right)_{p}=-\frac{\partial s}{\partial p}_{T}\)

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15

2014 · Engineering Sciences · Thermodynamic Relations · Thermodynamic Potentials and Property Relations

Engineering Sciences (XE) 2014

The equation of state for a certain gas is given by \(v = RT / P - C_1 / T^2 + C_2\), where \(C_1\) is 50,000 (K³.m³)/kg and \(C_2\) is 0.8 m³/kg. The relation \(\left(\frac{\partial h}{\partial P}\right)_T = v - T \left(\frac{\partial v}{\partial T}\right)_p\) is known for the gas. The inversion temperature, given by the condition, \(\left(\frac{\partial h}{\partial P}\right)_T = 0\) is __________ K.

A

500.0

B

433.0

C

353.6

D

250.0

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16

2015 · Engineering Sciences · Thermodynamic Relations · Thermodynamic Potentials and Property Relations

Engineering Sciences (XE) 2015

For a real gas undergoing volume expansion through a porous plug with \(\alpha = \frac{1}{v}\left(\frac{\partial v}{\partial T}\right)_p\), the Joule-Thomson cooling effect is observed if
(A) \(0 < \alpha T < 1\)
(B) \(\alpha T = 1\)
(C) \(\alpha T > 1\)
(D) \(\alpha T = 0\)

A

\(0 < \alpha T < 1\)

B

\(\alpha T = 1\)

C

\(\alpha T > 1\)

D

\(\alpha T = 0\)

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17

2016 · Engineering Sciences · Thermodynamic Relations · Thermodynamic Potentials and Property Relations

Engineering Sciences (XE) 2016

The Maxwell relation that results from the expression for the Helmholtz free energy \(A = U - TS\), is:

A

\(\left(\frac{\partial T}{\partial V}\right)_S = -\left(\frac{\partial P}{\partial S}\right)_V\)

B

\(\left(\frac{\partial T}{\partial P}\right)_S = \left(\frac{\partial V}{\partial S}\right)_P\)

C

\(\left(\frac{\partial P}{\partial T}\right)_V = \left(\frac{\partial S}{\partial V}\right)_T\)

D

\(\left(\frac{\partial V}{\partial T}\right)_P = -\left(\frac{\partial S}{\partial P}\right)_T\)

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18

2017 · Engineering Sciences · Thermodynamic Relations · Thermodynamic Potentials and Property Relations

Engineering Sciences (XE) 2017

Given the thermodynamic functional relations: \( p = p(v,T) \) and \( T = T(p,v) \), the term \( \frac{\partial p}{\partial v} \bigg|_T \times \frac{\partial v}{\partial T} \bigg|_p \) is equal to

A

\(- \left( \frac{\partial T}{\partial p} \bigg|_v \right)^{-1} \)

B

\(\left( \frac{\partial T}{\partial p} \bigg|_v \right)^{-1} \)

C

\(\left( \frac{\partial T}{\partial p} \bigg|_v \right) \)

D

1

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19

2017 · Engineering Sciences · Thermodynamic Relations · Thermodynamic Potentials and Property Relations

Engineering Sciences (XE) 2017

Given $d\phi = f(T)dT + (T/V)dV$ and $d\psi = Tdp + (T/p^2)dV$, then

A

both $\phi$ and $\psi$ are properties

B

neither $\phi$ nor $\psi$ is a property

C

$\phi$ is a property but $\psi$ is not a property

D

$\psi$ is a property but $\phi$ is not a property

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20

2018 · Engineering Sciences · Thermodynamic Relations · Thermodynamic Potentials and Property Relations

Engineering Sciences (XE) 2018

A gas obeys the following equation of state:
\( P(\bar{v}-b)=R T+\frac{a P^{2}}{T} \), where \( \bar{v} \) is molar volume, and \( a \), \( b \) are constants with values \( a=10^{-5} \mathrm{~J} . \mathrm{K} / \mathrm{Pa}^{2} \cdot \mathrm{kmol} \) and \( b=8 \times 10^{-2} \mathrm{~m}^{3} / \mathrm{kmol} \). Take \( C_{p}=30 \mathrm{~kJ} / \mathrm{kmol} . \mathrm{K} \). At 10 bar and 500 K, the value of the Joule-Thomson coefficient (in K/Pa) is

A

\(-2 \times 10^{-6} \)

B

\(-4 \times 10^{-6} \)

C

\(2 \times 10^{-6} \)

D

\(4 \times 10^{-6} \)

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