Final answer:
In a reversible isothermal process for an ideal gas, the temperature remains constant, and the work done is equal to the heat transferred, with no change in internal energy.
Step-by-step explanation:
When one mole of an ideal gas undergoes a reversible isothermal expansion or compression, several key thermodynamic quantities are involved. Isothermal means that the process occurs at a constant temperature. Using the ideal gas law, PV = nRT where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin. For an isothermal process, the temperature T remains constant while the volume V and pressure P may change.
The work W done by the gas during an isothermal expansion can be determined by integrating PdV over the change in volume, which gives W = nRT ln(Vf / Vi). Since the internal energy change ΔU of an ideal gas is dependent on temperature and the temperature remains constant in an isothermal process, therefore ΔU = 0.
During this isothermal process, the amount of heat Q added or removed from the system is equal to the work done by or on the gas, which is Q = W. This is in accordance with the first law of thermodynamics: ΔU = Q - W.