Chemical Thermodynamics Question 40

Question: Equal volumes of monoatomic and diatomic gases at same initial temperature and pressure are mixed. The ratio of specific heats of the mixture $ (C_{p}/C_{v}) $ will be [AFMC 2002]

Options:

A) 1

B) 2

C) 1.67

D) 1.5

Show Answer

Answer:

Correct Answer: D

Solution:

$ C_{v}=\frac{3}{2}RT;C_{p}=\frac{5}{2}RT $ for monoatomic gas

$ C_{v}=\frac{5}{2}\text{RT;},C_{p}=\frac{7}{2}RT $ for diatomic gas

Thus for mixture of 1 mole each, $ C_{v}=\frac{\frac{3}{2}RT+\frac{5}{2}RT}{2} $ and $ C_{p}=\frac{\frac{5}{2}RT+\frac{7}{2}RT}{2} $

Therefore, $ C_{p}/C_{v}=\frac{3RT}{2RT}=1.5 $ .



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