An ideal gas expands isothermally at temperature T from volume V₁ to V₂ via two different paths: Path I: Reversible isothermal expansion Path II: Isothermal free expansion (against vacuum) Consider the following statements regarding these two paths: (a) The change in internal energy ( U ) of the gas is zero for both paths. (b) The change in entropy of the system ( S_ system ) is the same for both paths. (c) The chang

Step-by-step solution

For an ideal gas undergoing an isothermal process, the change in internal energy ( U ) depends only on temperature. Since temperature is constant for both paths, U = 0 for both. Thus, statement (a) is correct. Entropy is a state function. Since both paths operate between the same initial and final states, the change in entropy of the system ( S_ system ) is identical for both paths. Thus, statement (b) is correct. The change in entropy of the surroundings ( S_ surroundings ) depends on the actual heat exchanged. Fo