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  • A gas is compressed adiabatically till its temperature is doubled. The ratio of its final volume to initial volume will beOption: 1 <img alt="1 / 2"

A gas is compressed adiabatically till its temperature is doubled. The ratio of its final volume to initial volume will be

Option: 1

1 / 2


Option: 2

more than 1 / 2


Option: 3

 less than 1 / 2


Option: 4

between 1 and 2


Answers (1)

best_answer

In adiabatic process, \mathrm{\quad p V^{\gamma}= constant}

Since, \mathrm{pV= RT}
Hence, \mathrm{TV^{\gamma -1}= k}

\mathrm{\Rightarrow t_{1}V_{1}^{\gamma }= T_{2}V_{2}^{\gamma -1}}
\mathrm{\Rightarrow \left(\frac{V_{2}}{V_{1}}\right)^{\gamma-1}=\left(\frac{T_{1}}{T_{2}}\right)=\frac{1}{2}}
\mathrm{\Rightarrow \quad \frac{V_{2}}{V_{1}}=\left(\frac{1}{2}\right)^{\frac{1}{\gamma-1}}}
Hence, ratio will be more than \mathrm{\frac{1}{2}}.

Posted by

himanshu.meshram

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