Question

4.0 g of helium occupies 22400 cm at STP.The specific heat capacity of helium at constant pressure is $5.0cal{K}^{-1}mo{l}^{-1}$. Calculate the speed of sound in helium at STP.

Answer 1

Speed of sound in helium$=\frac{969}{5}m/s.$

Given that 4.0 g of helium occupies 22400 cm³ at STP

The specific heat capacity of helium at constant pressure $=5.0cal{K}^{–1}mo{l}^{–1}=21J{K}^{–1}mo{l}^{–1}$

$Cp=\frac{\gamma R}{\gamma -1}$

=> $21\gamma -21=8.314\gamma$

=> $\gamma =\frac{21}{12.686}=1.65$

The velocity of sound will in the gas will be -

$\sqrt{\frac{\gamma RT}{M}}=\sqrt{\frac{\gamma PV}{M}}$

Pressure of the gas at STP, $P=1.013\times {10}^{5}pascal$

Volume of the gas , $V=22400\times {10}^{-6}$

mass of the gas ,$M=\frac{4}{1000}Kg$

Using the formula -

$Velocity=\sqrt{\frac{1.65\times 1.013\times {10}^5\times 22400\times {10}^{-}6}{0.004}}$

Velocity $=969.05$ m/s

The speed of sound in helium $=969.05$ m/s.