Relation Between Cp and Cv

Relation Between Cp and Cv MDCAT MCQs with answers

10 past paper MCQs on Relation Between Cp and Cv, from the Thermodynamics unit of MDCAT Physics. The year each question appeared is shown where known; tap “Show answer” for the correct option and a short solution.

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1.An ideal gas has molar specific heat $C_p$ at constant pressure. When the temperature of $n$ moles is increased by $\Delta T$, the increase in the internal energy is: (MDCAT 2023)

  1. $nC_p\Delta T$
  2. $n(C_p+R)\Delta T$
  3. $n(C_p-R)\Delta T$
  4. $n(2C_p+R)\Delta T$
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Correct answer: (c) $n(C_p-R)\Delta T$

$\Delta U=nC_v\Delta T$ and $C_p-C_v=R$, so $C_v=C_p-R$.

2.At a constant Pressure (Cp) and Volume (Cv), an ideal gas has C p - C v = R Then Cp will be? (KMU MDCAT 2025)

  1. R/2
  2. 3/2 R
  3. 5/2 R
  4. 7/2 R
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Correct answer: (c) 5/2 R

For a monatomic ideal gas $C_v=\tfrac32R$, so $C_p=C_v+R=\tfrac52R$.

3.For a monatomic ideal gas of 3 mole, Cp -Cv is: (PMC MDCAT 2022)

  1. R/3
  2. 3/2 R
  3. 2R
  4. 3R
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Correct answer: (d) 3R

$C_p-C_v=R$ for each mole, so for three moles it is $3R$.

4.The value of Cp and Cv is the same for: (PMC MDCAT 2022)

  1. He
  2. Ar
  3. Aluminium
  4. Neon
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Correct answer: (c) Aluminium

A solid barely changes volume on heating, so it does almost no work and its two heat capacities are the same.

5.If Cp = 20 J/mol.K then for 1 mole gas we get Cv= _______. You can use Cp/Cv = 1.7. (PMC MDCAT 2022)

  1. 10.6 J/K.mole
  2. 2.7 J/K.mole
  3. 13 J/K.mole
  4. 11.7 J/K.mole
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Correct answer: (d) 11.7 J/K.mole

$C_v=C_p/\gamma=20/1.7$, about $11.7\,\mathrm{J\,mol^{-1}\,K^{-1}}$.

6.Cp for monatomic gas in terms of R is: (PMC MDCAT 2022)

  1. 3/5 R
  2. 5/3 R
  3. 5/4 R
  4. 5/2 R
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Correct answer: (d) 5/2 R

For a monatomic gas $C_v=\tfrac32R$, so $C_p=\tfrac52R$.

7.For a monatomic ideal gas of 6 mole Cp/Cv: (PMC MDCAT 2022)

  1. 1.4
  2. 1.67
  3. 5
  4. 3
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Correct answer: (b) 1.67

For a monatomic gas $\gamma=\tfrac52R/\tfrac32R$, that is $1.67$, whatever the amount.

8.Cp = 49 J/K.mole and Cv= 35 J/K,mol then what type of gas Is this? (PMC MDCAT 2022)

  1. Diatomic
  2. Monatomic
  3. Triatomic
  4. Nonlinear-triatomic
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Correct answer: (a) Diatomic

$C_p-C_v=14$, about $R$, and $C_p/C_v=1.4$, which is the value for a diatomic gas.

9.If Cv= 5/2 R , Cpwill be: (UHS MDCAT 2018)

  1. 2 / 5 R
  2. 2 / 7 R
  3. 5 / 2 R
  4. 7 / 2 R
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Correct answer: (d) 7 / 2 R

$C_p=C_v+R=\tfrac52R+R$, that is $\tfrac72R$.

10.If one mole of an ideal gas is heated at constant pressure, then the first law of thermodynamics can be written as: (UHS MDCAT 2018)

  1. CpΔT = CvΔT + PΔV
  2. CvΔT = CpΔT + PΔV
  3. CpΔT = CvΔT + VΔP
  4. ΔCpT = ΔCvT + PΔV
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Correct answer: (a) CpΔT = CvΔT + PΔV

The heat put in at constant pressure raises the internal energy and does the work $P\Delta V$.

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