Kinetic Theory Of Gases Question 86
Question: 4.0 g of a gas occupies 22.4 liters at NTP. The specific heat capacity of the gas at constant volume is $ 5.0J{{K}^{-1}}. $ If the speed of sound in this gas at NTP is $ 952m{{s}^{-1}}, $ then the heat capacity at constant pressure is (Take gas constant $ R=8.3J{{K}^{-1}}mo{{l}^{-1}} $ )
Options:
A) $ 7.5J{{K}^{-1}}mo{{l}^{-1}} $
B) $ 7.0J{{K}^{-1}}mo{{l}^{-1}} $
C) $ 8.5J{{K}^{-1}}mo{{l}^{-1}} $
D) $ 8.0J{{K}^{-1}}mo{{l}^{-1}} $
Show Answer
Answer:
Correct Answer: D
Solution:
[d] Molar mass of the gas = 4g/mol Speed of sound $ V=\sqrt{\frac{\gamma RT}{m}}\Rightarrow 952=\sqrt{\frac{\gamma \times 3.3\times 273}{4\times {{10}^{-3}}}} $
$ \Rightarrow ,\gamma =1.6=\frac{16}{10}=\frac{8}{5} $ Also, $ \gamma =\frac{C _{P}}{C _{v}}=\frac{8}{5} $
$ \text{So, }C _{p}=\frac{8\times 5}{5}=8J{{K}^{-1}}mo{{l}^{-1}} $
$ [ C _{v}=5.0J{{K}^{-1}}given ] $
BETA
