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

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

COMEDKCOMEDK 2006Thermodynamics

Solution:

For adiabatic process, $PV^{\gamma}$ =constant
or, $\left(\frac{nRT}{V}\right)V^{\gamma}$ = constant
or, $ T V^{\left(\gamma -1\right)}$ = constant
$\therefore \:\: T_{1}V_{1}^{\left(\gamma -1\right)} = T_{2} V_{2}^{\left(\gamma -1\right)} $
Here, $T_{2} = 2T_{1} $
So,$ 2T_{1}V_{2}^{\left(\gamma -1\right)} = T_{1}V_{1}^{\left(\gamma -1\right)}$
or, $ \frac{V_{1}}{V_{2}} = \left(2\right)^{1 \left(\gamma -1\right)} > 2 $