Question
One mole of a real gas is subjected to heating at constant volume from (P1, V1, T1) state to (P2, V1, T2) state. Then it is subjected to irreversible adiabatic compression against constant external pressure of P3 atm, till the system reaches final state (P3, V2, T3). If the constant volume molar heat capacity of real gas is CV, then the correct expression for ΔH from State 1 to State 3 is
Options
Solution
$\Delta U_{1} = n.C_{V,m}.\left( T_{2} - T_{1} \right)$
$\Delta H_{1} = \Delta U_{1} + V.\Delta P = 1 \times C_{V,m} \times \left( T_{2} - T_{1} \right) + V_{1}\left( P_{2} - P_{1} \right)$
$\text{Now, }\Delta U_{2} = w_{2} = - P_{ext}\left( V_{2} - V_{1} \right) = - P_{3}\left( V_{2} - V_{1} \right) $$${\Delta H_{2} = \Delta U_{2} + \Delta(PV) = - P_{3}\left( V_{2} - V_{1} \right) + \left( P_{3}V_{2} - P_{2}V_{1} \right) }{\therefore\Delta H_{\text{total}} = \Delta H_{1} + \Delta H_{2} = C_{V}\left( T_{2} - T_{1} \right) + V_{1}\left( P_{3} - P_{1} \right)}$$
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