Project ForgeProcess Calculations
Laws of Thermodynamics
GATE 2014
Hard
Which ONE of the following is CORRECT for an ideal gas in a closed system?
- A(∂U/∂V)_S·V = nR(∂U/∂S)_V
- B−(∂H/∂P)_S·P = nR(∂H/∂S)_P
- C(∂U/∂V)_S·V = nR(∂H/∂S)_P
- (∂H/∂P)_S·P = nR(∂U/∂S)_V
Explanation
From dU=TdS−PdV: (∂U/∂V)_S=−P and (∂U/∂S)_V=T. From dH=TdS+VdP: (∂H/∂P)_S=V and (∂H/∂S)_P=T. Option D gives (V)(P)=nR(T), i.e. PV=nRT — exactly the ideal gas law, so it is correct. (Options A, B, C all reduce to −PV=nRT, which is false.)
Source: GATE CH 2014 (2014)
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