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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 broght to rest. Assuming no heat is lost to the surroundings, its temperature increases by
A
$\frac{{\gamma M{v^2}}}{{2R}}K$
B
$\frac{{\left( {\gamma - 1} \right)}}{{2R}}M{v^2}K$
C
$\frac{{\left( {\gamma - 1} \right)}}{{2\left( {\gamma + 1} \right)R}}M{v^2}K$
D
$\frac{{\left( {\gamma - 1} \right)}}{{2\gamma R}}M{v^2}K$
Solution
$\mathrm{W}=\mathrm{J} . \mathrm{H}$
$\frac{1}{2} \mathrm{mv}^{2}=\mathrm{J} . \mathrm{n.} \mathrm{C}_{\mathrm{V}} \mathrm{dT}$
$\frac{1}{2} \mathrm{mv}^{2}=\mathrm{J} \cdot \frac{\mathrm{m}}{\mathrm{M}} \cdot \frac{\mathrm{R}}{(\gamma-1)} \cdot \mathrm{dT}$
Standard 11
Physics
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