An ideal gas ( n moles) expands isothermally and irreversibly from an initial volume V₁ to a final volume V₂ against a constant external pressure P_ ext at temperature T . Which of the following represents the correct mathematical expressions for the entropy change of the system ( S_ sys ) and the surroundings ( S_ surr )?

Step-by-step solution

Entropy is a state function, meaning its change for the system depends only on the initial and final states, not the path taken. For an ideal gas undergoing isothermal expansion, the entropy change is calculated using a reversible path: S_ sys = nR ( V₂ V₁ ) . The entropy change of the surroundings depends on the actual heat exchanged. In this irreversible process against a constant external pressure, the work done by the system is w = -P_ ext (V₂ - V₁) . Since the process is isothermal for an ideal gas, U = 0 . Ac