Final answer:
For an isothermal process, the first law of thermodynamics can be expressed as ΔU = Q - W, which simplifies to Q = W since the change in internal energy (ΔU) is zero due to constant temperature.
Step-by-step explanation:
The mathematical equation for the first law of thermodynamics for an isothermal process can be simply stated as ΔU = Q - W, where ΔU stands for the change in internal energy, Q for the heat added to the system, and W for the work done by the system. In an isothermal process, the temperature of the system remains constant. As a consequence of constant temperature and the definition of internal energy, the change in internal energy (ΔU) of an ideal gas is zero. Therefore, according to the first law of thermodynamics, the heat input is equal to the work done, mathematically expressed as Q = W for an isothermal process within a closed system.
When we use this law practically, we can consider P-V diagrams, which visualize the processes undergone by the system, including isothermal, adiabatic, isobaric, and isochoric processes.
These conceptual tools highlight the relationships between pressure, temperature, and volume throughout thermodynamic processes.