A mass m of an ideal gas initially has volume Voand temperature To. When it is kept at constant volume Vo, heat Q is required to increase its temperature to To $$+$$ DT. If the volume is not kept constant, but the gas expands from Vo to $$3Vo$$ when the temperature increases from To to (To$$ $$+$$ $$2DT), then the heat supplied must be

Question

A mass m of an ideal gas initially has volume Voand temperature To.  When it is kept at constant volume Vo, heat Q is required to increase its temperature to To $$+$$ DT.  If the volume is not kept constant, but the gas expands from Vo to $$3Vo$$ when the temperature increases from To to (To$$ $$+$$ $$2DT), then the heat supplied must be

Infinity Learn · Accepted Answer

In the first case the rise in temperature is ΔT and in the second case it is $$2$$ΔT. The heat required for this must be $$2Q$$. In addition to rising the temperature, the system is expanding and doing work and additional heat will be required for this, hence more than $$2QNumber$$ of moles, n $$=$$ $$m/M$$.In he first case. Q $$=$$ $$nCv(Tf$$ $$-$$ $$Ti)In$$ the second case, from $$1st$$ law of thermodynamics,

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