An ideal gas expands isothermally at temperature T from an initial volume V₁ to a final volume V₂ against a constant external pressure P_ ext . Which of the following expressions correctly represents the change in entropy of the surroundings ( S_ surroundings ) for this process?

Step-by-step solution

For an irreversible expansion against a constant external pressure P_ ext , the work done by the system is given by W = -P_ ext (V₂ - V₁) . Since the process is isothermal for an ideal gas, the change in internal energy is zero ( U = 0 ). According to the first law of thermodynamics, U = q_ sys + W . Therefore, the actual heat absorbed by the system is q_ sys = -W = P_ ext (V₂ - V₁) . The heat absorbed by the surroundings is the negative of the heat absorbed by the system: q_ surr = -q_ sys = -P_ ext (V₂ - V₁) . Th