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The answer is that when the temperature rises of the gas, the pressure goes up and it pushes the mercury down, but then the tube on the right is lifted up by the person operating the experiment to increase the pressure on the gas and return it to its original volume - so the height h increases. The reason that there is flexible tube at the bottom fo the ...


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Thank you joshphysics for this wonderful answer. I myself was confused like Sanyia. I just wanted to add in a point on what caused this confusion. In the left-hand side of the equation, when we see the term $cv$, we automatically assume that the all terms should have this same condition. But this is wrong because joshphysics pointed out that $$(dE/dT)v dT + ...


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Actually, that is not the correct formula for gases. In the usual model of ideal gases, the volume is given as a function of both temperature and pressure by the equation: $$V=\frac{n\bar RT}{p}$$ Both formulas you wrote are valid for solids and liquids (but not for gases). In those phases, volume is much more affected by temperature than by pressure, so ...



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