Is temperature a frame-dependent quantity?
Question:
A thermally insulated vessel contains an ideal gas of molecular mass $M$ and ratio of specific heats $\gamma$. It is moving with speed $v$ and is suddenly brought to rest. Assuming no heat is lost to the surroundings, by how much does its temperature increase?
Solution:
$\frac{1}{2}Mv^2 = (\gamma-1) nR \Delta T \\ \implies \Delta T = \frac{(\gamma-1)Mv^2}{2R}$
What if we observe the whole process from an inertial frame of reference moving with some velocity? Then, clearly, a factor involving velocity of frame remains, meaning that the difference in temperature would depend on the frame of reference, which is absurd. So where does my reasoning go wrong?
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