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  • If c is r.m.s speed of molecules in a gas and v is the speed of sound waves in the gas, show that c/v is constant and independent of temperature for all diatomic gases.

If c is r.m.s speed of molecules in a gas and v is the speed of sound waves in the gas, show that c/v is constant and independent of temperature for all diatomic gases.

Answers (1)

We know that c= \sqrt{\frac{3P}{\rho}} for molecules 

c= \sqrt{\frac{3RT}{M}}

\frac{p}{\rho}=\frac{PT}{M} where M is the molar mass of gas 

\frac{P}{\rho}=\frac{\frac{RT}{V}}{\frac{M}{V}}

v=\frac{\gamma P}{\rho}=\frac{\gamma RT}{M}

PV=nRT When n=1

P=\frac{RT}{V}cv=\sqrt{\frac{\frac{3RT}{M}}{\frac{\gamma RT}{M}}} ={\sqrt{}\frac{3}{\gamma }} 

c/v=\sqrt{\frac{\frac{3RT}{M}}{\frac{\gamma RT}{M}}} ={\sqrt{}\frac{3}{\gamma }}

\gamma =\frac{C_{p}}{C_{v}}=\frac{7}{5}adiabatic constant for diatomic gas 

\frac{c}{v}= \sqrt{\frac{15}{7}}=constant 

Posted by

infoexpert24

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