Q. 4.0 g of a gas occupies 22.4 litres at NTP. The specific heat capacity of the gas at constant volume is 5.0 $JK^{-1}mol^{-1}$. If the speed of sound in this gas at NTP is 952 $ms^{-1}$, then the heat capacity at constant pressure is (Take gas constant R = 8.3 $JK^{-1}mol^{-1}$)
A) 8.5 $JK^{-1}mol^{-1}$
B) 8.0 $JK^{-1}mol^{-1}$
C) 7.5 $JK^{-1}mol^{-1}$
D) 7.0 $JK^{-1}mol^{-1}$
Explanation
[Solution] M = 4 g/mol; $\gamma = \frac{Mv^2}{RT} = \frac{0.004 \times 952^2}{8.3 \times 273} \approx 1.6$, so $C_p = \gamma C_v = 8.0$. Answer (2).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.