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A perfectly insulated container holds an ideal gas whose molecular mass is M and whose ratio of specific heats is γ. If the container is moving with speed v and is then stopped abruptly, with no heat exchange with the surroundings, the rise in the gas temperature is

1. ((γ − 1)/(2γR)) Mv² K
2. (γMv²)/(2R) K
3. ((γ − 1)/(2R)) Mv² K
4. ((γ − 1)/(2(γ + 1)R)) Mv² K

Correct answer: ((γ − 1)/(2R)) Mv² K

Solution

Kinetic energy converts to internal energy: (1/2)*(n*M)*v^2 = n*(R/(gamma-1))*dT. Solving gives dT = (gamma-1)*M*v^2/(2R).

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