An insulated box containing a diatomic gas of molar mass m is moving with velocity v . box

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11.Thermodynamics

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An insulated box containing a diatomic gas of molar mass $m$ is moving with velocity $v$. The box is suddenly stopped. The resulting change in temperature is :-

$\frac{mv^2}{2R}$

$\frac{mv^2}{3R}$

$\frac{mv^2}{5R}$

$\frac{2mv^2}{5R}$

Solution

Apply energy conservation

work done $=$ loss in kinetic energy

$\frac{\mu \mathrm{R}}{(\mathrm{Y}-1)}\left(\mathrm{T}_{1}-\mathrm{T}_{2}\right)=\frac{1}{2} \mathrm{mV}^{2}$

$\left(\frac{\mathrm{M}}{\mathrm{m}}\right) \frac{\mathrm{R}\left(\mathrm{T}_{1}-\mathrm{T}_{2}\right)}{\left(\frac{7}{5}-1\right)}=\frac{1}{2} \mathrm{MV}^{2}$

Hence $\mathrm{T}_{1}-\mathrm{T}_{2}=\Delta \mathrm{T}=\frac{\mathrm{mV}^{2}}{5 \mathrm{R}}$

Standard 11

Physics

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An insulated box containing a diatomic gas of molar mass $m$ is moving with velocity $v$. The box is suddenly stopped. The resulting change in temperature is :-

Solution

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