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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 is suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by
A
$\frac{{(\gamma - 1)}}{{2\left( {\gamma + 1} \right)R}}M{v^2}$
B
$\frac{{(\gamma - 1)}}{{2\gamma R}}M{v^2}$
C
$\frac{{\gamma M{v^2}}}{{2R}}$
D
$\frac{{(\gamma - 1)}}{{2R}}M{v^2}$
Solution
Total kinetic energy will increase temperature
$\mathrm{K.E.}$ $=\Delta \mathrm{U}$
$\Rightarrow \frac{1}{2}(\mathrm{nM}) \mathrm{V}^{2}=\frac{\mathrm{nR} \Delta \theta}{\gamma-1}$
$\mathrm{n}=$ number of moles.
$\boxed{\Delta \theta = \frac{{{\text{M}}{{\text{v}}^2}(\gamma – 1)}}{{2{\text{R}}}}}$
Standard 11
Physics
