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12.Kinetic Theory of Gases
normal
A thermally insulated vessel contains an ideal gas of molecular mass $M$ and ratio of specific heats $\gamma $. It is moving with speed $v$ and its suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature` increases by
A
$\frac{{(\gamma - 1)}}{{2\gamma R}}M{v^2}K$
B
$\frac{{\gamma M{v^2}}}{{2R}}K$
C
$\frac{{(\gamma - 1)}}{{2R}}M{v^2}K$
D
$\frac{{(\gamma - 1)}}{{2(\gamma + 1)R}}M{v^2}K$
Solution
As no heat is lost,
Loss of kinetic energy $=$ gain of internal energy of gas
$ \frac{1}{2} m v^{2}=n C_{V} \Delta T$
$\Rightarrow \quad \frac{1}{2} m v^{2}=\frac{m}{M} \cdot \frac{R}{\gamma-1} \Delta T$
$\Rightarrow \quad \Delta T=\frac{m v^{2}(\gamma-1)}{2 R} K$
Standard 11
Physics
