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  4. A diatomic gas initially at 18° C is compressed adiabatically to one eighth of its original volume. The temperature after compression will be

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Q. A diatomic gas initially at $18^{\circ} C $ is compressed adiabatically to one eighth of its original volume. The temperature after compression will be

AIPMTAIPMT 1996

Solution:

Initial temperature $(T_1)=18^0C$
= (273 + 18) = 291 K and $V_2=(1/8)V_1. $
For adiabatic compression, $TV^{\gamma-1}=constant $
or $T_1V_1^{\gamma-1}= T_2V_2^{\gamma-1} .$
Therefore $T_2=T_1 \bigg (\frac {V_1}{V_2}\bigg )^{\gamma-1}$
$ =291 \times (8)^{1.4-1}=291 \times (8)^{0.4} $
$ =291 \times 2.297=668.4 K=395.4^0C. $