Gujarati
Hindi
11.Thermodynamics
normal

A perfect gas is found to obey the relation $PV^{3/2} =$ constant, during an adiabatic process. If such a gas, initially at a temperature $T$, is compressed adiabatically to half its initial volume, then its final temperature will be

A

$2\,\,T$

B

$4\,\,T$

C

$\sqrt 2 \,\,T$

D

$2\sqrt 2 \,\,T$

Solution

$\mathrm{PV}^{3 / 2}=$ Constant $, \mathrm{PV}$

$=\mathrm{RT}$ or $\mathrm{P}=\frac{\mathrm{RT}}{\mathrm{V}}$

$\left(\frac{\mathrm{RT}}{\mathrm{V}}\right) \times \mathrm{V}^{3 / 2}=$ Constant

or $\mathrm{TV}^{1 / 2}=$ Constant

$\therefore$ Thus $V$ changes to $V / 2,$ the temp. becomes $\sqrt{2} T$

Standard 11
Physics

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