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I was thinking about a situation where some gas is enclosed inside a container and kept in a train at rest. The train accelerates, gains a maximum speed and then suddenly stops. Would the temperature of the gas change during this process?

I know that temperature is directly proportional to average kinetic energy of gas molecules but would the train during this process change the kinetic energy of the gas molecules inside the closed container?

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In principle, YES.

Remember, temperature is related to the velocity distribution of the particles inside the gas. The key word here is $collision$.

Accelerating the train and suddenly stopping it is akin to shaking a container that contains fluid once. The sudden acceleration and deceleration of the contained will impart momentum from the wall of the container to the particles inside. I see two cases.

(a) If the container contains liquid and is not completely full, you could increase its temperature because you are imparting momentum of the particles inside the liquid by virtue of them sloshing inside the container.

(b) If the container contains liquid and is completely full, you could increase its temperature in the same principle but not significantly. Similarly, for a gas, while in principle you could have the same effect as in a container filled with gas, the density of the gas is so much lower than the liquid, the effect would have to be negligible.

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The temperature is the kinetic energy of the gas molecules within the container. if you can measure the slightest of slightest variation in temperature of gas, then you will find temperature has increased. Train will rise the temperature of gas just by shaking it during travelling (Friction) and also when you suddenly stop the train, the gas slam on the containers one side & sudden buildup of pressure on the side causes temperature of the gas to go higher locally. Gas laws is applied here as the volume is fixed and change in pressure causes temperature to rise.

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