For an ideal gas, starting from state point 1, two different processes take place. The corresponding final states in these two processes 2 and 3, lying on same isotherm. If P and h represent pressure and enthalpy, respectively, then which one of the following is correct?

The correct option is h₂ = h₃.

To understand why this is correct, we can analyze the thermodynamic properties of an ideal gas.
For an ideal gas, enthalpy (h) is a function of temperature (T) only. This relationship is defined by Joule's law of thermodynamics, which states:
$$h=f\left(T\right)$$ Specifically, the change in enthalpy is given by:
$$dh=C_{p}dT$$ where _Cp is the specific heat capacity at constant pressure, and dT is the change in temperature.

The problem states that the final states 2 and 3 lie on the same isotherm.
An isotherm is a line or curve of constant temperature. Therefore, the temperature at state 2 is equal to the temperature at state 3:
$$T_2=T_3$$

Since the enthalpy of an ideal gas depends solely on its temperature, and states 2 and 3 are at the same temperature, their enthalpies must be equal:
$$h_2=h_3$$ Thus, the relationship h₂ = h₃ holds true regardless of the paths taken to reach these states from state 1, or their final pressures.