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Concepts Of Physics MCQ Edition [Volume 2]
Exam
Concepts Of Physics MCQ Edition [Volume 2]
Subject
Physics
Chapter
Specific Heat Capacities of Gases

Concepts Of Physics MCQ Edition [Volume 2] · Physics · Specific Heat Capacities of Gases

An ideal gas has a molar heat capacity ratio of C_p / C_V = 7/6 ....

An ideal gas has a molar heat capacity ratio of Cp/CV=7/6C_p / C_V = 7/6. Determine the change in internal energy of 1.01.0 mole of this gas when its temperature is raised by 50 K50 \text{ K} while keeping the pressure constant.

Options

  1. A2905 J2905 \text{ J}
  2. B2075 J2075 \text{ J}
  3. C2490 J2490 \text{ J}
  4. D415 J415 \text{ J}

Correct answer

C. 2490 J2490 \text{ J}

Step-by-step solution

Given CpCV=76\dfrac{C_p}{C_V} = \dfrac{7}{6}

For an ideal gas, Cp−CV=RC_p - C_V = R

76CV−CV=R⇒16CV=R⇒CV=6R\dfrac{7}{6}C_V - C_V = R \Rightarrow \dfrac{1}{6}C_V = R \Rightarrow C_V = 6R

The change in internal energy of an ideal gas depends only on the change in temperature and is given by ΔU=nCVΔT\Delta U = n C_V \Delta T

Substituting n=1 moln = 1 \text{ mol}, CV=6RC_V = 6R, and ΔT=50 K\Delta T = 50 \text{ K}:

ΔU=1×6R×50=300R\Delta U = 1 \times 6R \times 50 = 300R

Using R=8.3 J mol−1 K−1R = 8.3 \text{ J mol}^{-1} \text{ K}^{-1}:

ΔU=300×8.3=2490 J\Delta U = 300 \times 8.3 = 2490 \text{ J}
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