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11.Thermodynamics
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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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