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  • An ideal gas is expanded adiabatically. How many times has the gas to be expanded to reduce the

An ideal gas (\gamma=1.5) is expanded adiabatically. How many times has the gas to be expanded to reduce the root mean square velocity of molecules 2.0 times

Option: 1

 4 times


Option: 2

16 times


Option: 3

8 times


Option: 4

2 times


Answers (1)

\quad \mathrm{V}_{\mathrm{rms}}=\sqrt{\frac{3 \mathrm{RT}}{\mathrm{M}}}
\therefore \quad \mathrm{V}_{\mathrm{rms}} \propto \sqrt{\mathrm{T}}

\mathrm{V_{r m s}} is to reduce two times i.e, temperature of the gas will have to reduce four times or
\frac{\mathrm{T}^{\prime}}{\mathrm{T}}=\frac{1}{4}

During adiabatic process

\mathrm{TV}^{\gamma-1}=\mathrm{T}^{\prime} \mathrm{V}^{\prime \gamma-1}
\text { or, } \frac{\mathrm{V}^{\prime}}{\mathrm{V}}=\left(\frac{\mathrm{T}}{\mathrm{T}^{\prime}}\right)^{\frac{1}{\gamma-1}}=(4)^{\frac{1}{1.5-1}}=4^{2}=16
\therefore \quad \mathrm{V}^{\prime}=16 \mathrm{~V}

Hence, (B) is correct

Posted by

Ramraj Saini

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