An ideal gas (γ=1.5) is expanded adiabatically. How many times has the gas to be expanded to reduce the root mean square velocity of molecules 2…

Question

An ideal gas (γ=1.5) is expanded adiabatically. How many times has the gas to be expanded to reduce the root mean square velocity of molecules 2 times?

MARKS Content Team · Accepted Answer

Correct answer: (B) 16 times. v_rms=√3RTM or v_rms∝√T v_rms is to reduce two times, ie, the temperature of the gas will have to reduce four times or (T′)/T=1/4 During adiabatic process, TV^(γ-1)=T^(′)V^(′γ-1) or (V^(′))/V=T^(T′)1/(γ-1) =4^(11.5-1)=4^2=16 ∴ V^(′)=16 V

An ideal gas $(γ = 1.5)$ is expanded adiabatically. How many times has the gas to be expanded to reduce the root mean square velocity of molecules $2$ times?

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