Question 866: Thermodynamics & KTG

Question

An insulated container contains a monoatomic gas of molar mass '$$\mathrm{m}$$'. The container is moving with velocity '$$\mathrm{V}$$'. If it is stopped suddenly, the change in temperature of a gas is [R is gas constant]

Accepted Answer

Kinetic energy loss of the gas is
$$\Delta \mathrm{E}=\frac{1}{2} M V^2 \cdot \mathrm{n}$$ ..... (i) ....(where $$\mathrm{n}$$ is the no. of moles of the gas)
Heat  gained by the gas due to temperature change $$\Delta \mathrm{T}$$ is $$\Delta Q={ }_n C_V \Delta T
$$
But, $$\mathrm{C}_{\mathrm{V}}=\frac{3}{2} \mathrm{R}$$ ....(gas is monoatomic)
$$	herefore \quad \Delta \mathrm{Q}=\frac{3}{2} \mathrm{R} \cdot \mathrm{n} \Delta \mathrm{T}$$ ..... (ii)
Equating (i) and (ii),
$$\begin{aligned}
& \Delta \mathrm{E}=\Delta \mathrm{Q} \
& \frac{1}{2} \mathrm{MV}^2 \cdot \mathrm{n}=\frac{3}{2} \mathrm{R} \cdot \mathrm{n} \Delta \mathrm{T} \
& \Delta \mathrm{T}=\frac{\mathrm{MV}}{3 \mathrm{R}}
\end{aligned}$$

Answer

$$\frac{\mathrm{MV}^2}{\mathrm{R}}$$

Answer

$$\frac{M V^2}{2 R}$$

Answer

$$\frac{\mathrm{MV}^2}{3 \mathrm{R}}$$

Answer

$$\frac{3 \mathrm{MV}^2}{2 \mathrm{R}}$$

Thermodynamics & KTG

An insulated container contains a monoatomic gas of molar mass '$\mathrm{m}'. The container is moving with velocity '\mathrm{V}$'. If it is stopped suddenly, the change in temperature of a gas is [R is gas constant]

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