Internal energy change, when a system goes from state A and B is 40 kJ mole-1. If the system goes from A and B by a reversible path and returns to state A by an irreversible path, what would be the net change in internal energy?

Internal energy change, when a system goes from state A and B is 40 kJ mole-1. If the system goes from A and B by a reversible path and returns to state A by an irreversible path, what would be the net change in internal energy? Correct Answer Zero

As the system returns to the initial state A, the change in internal energy is zero.

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On a P-V diagram of an ideal gas, suppose a reversible adiabatic line intersects a reversible isothermal line at point A. Then at a point A, the slope of the reversible adiabatic line $${\left( {\frac{{\partial {\text{P}}}}{{\partial {\text{V}}}}} \right)_{\text{S}}}$$  and the slope of the reversible isothermal line $${\left( {\frac{{\partial {\text{P}}}}{{\partial {\text{V}}}}} \right)_{\text{T}}}$$  are related as (where, $${\text{y}} = \frac{{{{\text{C}}_{\text{p}}}}}{{{{\text{C}}_{\text{v}}}}}$$  )