An insulated container contains a monoatomic gas of molar mass ' $m$ '. The container is moving with…

An insulated container contains a monoatomic gas of molar mass ' $m$ '. The container is moving with velocity ' $V$ '. If it is stopped suddenly, the change in temperature is ( $\mathrm{R}=$ gas constant)
  1. $\frac{\mathrm{mV}^2}{5 \mathrm{R}}$
  2. $\frac{\mathrm{mV}^2}{3 \mathrm{R}}$
  3. $\frac{\mathrm{mV}^2}{7 \mathrm{R}}$
  4. $\frac{\mathrm{mV}^2}{9 \mathrm{R}}$

Solution

If the container stops suddenly loss in kinetic energy of gas $=\frac{1}{2}(\mathrm{mn}) \mathrm{V}^2$ For monoatomic gas, the change in internal energy of the gas is given by, $\Delta \mathrm{U}=\frac{3}{2} \mathrm{nR} \Delta \mathrm{~T}$
The change in kinetic energy is converted into internal energy, $\begin{aligned} & \therefore \quad \frac{3}{2} n R \Delta T=\frac{1}{2} \mathrm{mnV}^2 \\ & \therefore \quad \Delta \mathrm{~T}=\frac{\mathrm{mV}^2}{3 \mathrm{R}} \end{aligned}$

Asked in: MHT CET 2024 (04 May Shift 1)

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