An insulated container containing n moles of monoatomic gas of molar mass m is moving with a velocity v₀. If the container is suddenly stopped, find the changes in temperature

Correct Answer is : mv023Rm v₀²/3 R3Rmv02

Correct Answer is : mv023Rm v₀²/3 R3Rmv02

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NEET Exam Model Paper 7

Question : 9 of 180

Marks: +1, -0

v_0

Solution:

There is n moles of the monoatomic gas in the container.

Molar mass of the gas = m,

Total mass of the gas in the container, M = mn

Change in KE of the gas when the container is suddenly stopped, i.e.,

\Delta K = (KE)_{\text{initial}} - (KE)_{\text{final}} = \frac{1}{2} M v_0^2 - 0

=\frac{1}{2} M v_0^2 = \frac{1}{2} M v_0^2

This change in kinetic energy

(\Delta K)

result in a change in internal energy

(\Delta U)

of the gas

\Delta U = n C_v \Delta T = n \left( \frac{3}{2} R \right) \Delta T

Here,

\Delta T

is the change in temperature of the gas

\Delta U = \Delta K, n \left( \frac{3}{2} R \right) \Delta T = \frac{1}{2} m n v_0^2

\therefore \Delta T = \frac{m v_0^2}{3 R}

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