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  4. An ideal gas at 27° C is compressed adiabatically to 8/27 of its original volume. The rise in temperature is (Take γ =5/3)

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Q. An ideal gas at $27^{\circ} C $ is compressed adiabatically to 8/27 of its original volume. The rise in temperature is (Take $\gamma =5/3$)

AIPMTAIPMT 1999

Solution:

$TV^{\gamma-1}= $ constant (adiabatic).
$\, \, \, \, \, \, =(300)(V_0)^{2/3}=(V_f)^{2/3} T$
$T=300 \bigg (\frac {27}{8}\bigg )^{2/3} =300 \times \bigg (\frac {3}{2}\bigg )^{3 \times \frac {2}{3}}= \frac {300 \times 9}{4}= 675 K $
Temperature rise = 675-300=375 K