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  • An insulated container containing monoatomic gas of molar mass m is moving with a velocity v_0. If the container is suddenly stopped, find the change in temperature.

An insulated container containing monoatomic gas of molar mass m is moving with a velocity v_{0}. If the container is suddenly stopped, find the change in temperature.

Answers (1)

Since the gas is monoatomic, only translational degree of freedom will be applicable. KE per molecule = \frac{3}{2} R T. when the container which is insulated has suddenly stopped, a transfer of kinetic energy takes place to the gas molecules. Let \Delta T be the slight increase in temperature and n be the number of moles of gas.

The resultant increase in translational KE can be presented as,

KE = \frac{3}{2} n. R. \Delta T

Increased KE due to velocity,

v_{0} = \frac{1}{2} (m n) v_{0}^{2}

Hence,

\frac{mn}{2} v_{0}^{2}=\frac{3}{2} n. R. \Delta T

So,

\Delta T = \frac{m n v_{0}^{2} \times 2}{2 \times 3 \times n R} =\frac{ m v_{0}^{2}}{3R}

Posted by

infoexpert24

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