One mole of a real gas is heated at constant volume from (P 1 , V 1 , T 1 ) to (P 2 , V 1 , T 2 ). It is then compressed adiabatically and irreversibly against a constant external pressure P 3 until i

Question

One mole of a real gas is heated at constant volume from (P 1 , V 1 , T 1 ) to (P 2 , V 1 , T 2 ). It is then compressed adiabatically and irreversibly against a constant external pressure P 3 until it reaches (P 3 , V 3 , T 3 ). The molar heat capacity at constant volume, C V , is constant. The correct expression for Δ H from State 1 to State 3 is

TestHub · Accepted Answer

Δ H is a state function: Δ H = Δ U + Δ(PV) between State 1 and State 3. C V constant gives Δ U = C V (T 3 - T 1 ) regardless of path (heating step plus adiabatic step). Δ(PV) = P 3 V 3 - P 1 V 1 . So Δ H = C V (T 3 - T 1 ) + (P 3 V 3 - P 1 V 1 ). C P (T 3 - T 1 ) holds only for an ideal gas, and the (a) and (d) forms use wrong end temperatures or volumes. Matches (c).

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