Question
In the P-Vdiagram show, moles of a gas are taken through a process from state i to f, at constant pressure. Part of the heat must have gone into doing the work PΔV, and the rest in increasing the internal energy. If the molar specific heat at constant volume for the gas is CV, and the initial total internal energy is Ui, what is the final internal energy Uf?
Answer: Option D
:
D
: In the diagram, the two lines represent isotherms for temperatures T and (T+ΔT) - any point on either line will be at the same temperature. If a process takes the state of a gas from a point on one isotherm to a point on another isotherm, the change in internal energy will be related to the temperature difference only, and nothing else, given by the relation -
ΔEint=nCvΔT
Therefore in our case,
Uf=Ui+ΔEint
⇒Uf=Ui+nCvΔT.
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:
D
: In the diagram, the two lines represent isotherms for temperatures T and (T+ΔT) - any point on either line will be at the same temperature. If a process takes the state of a gas from a point on one isotherm to a point on another isotherm, the change in internal energy will be related to the temperature difference only, and nothing else, given by the relation -
ΔEint=nCvΔT
Therefore in our case,
Uf=Ui+ΔEint
⇒Uf=Ui+nCvΔT.
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