Enthalpy is a thermodynamic property that represents the total heat content of a system. It is denoted by the symbol H and is defined as the sum of the internal energy (U) of the system plus the product of the pressure (P) and volume (V) of the system.

In a closed system, no mass is exchanged with the surroundings. Therefore, any change in the enthalpy of the system can only occur through the transfer of heat or work. The change in enthalpy is given by the equation:

ΔH = Q + W

where ΔH is the change in enthalpy, Q is the heat transferred to the system, and W is the work done on or by the system.

In a reversible process, the system undergoes a series of equilibrium states, where the system and surroundings are always in thermodynamic equilibrium. This means that the system can be brought back to its initial state by reversing the process without leaving any trace.

The change in enthalpy for a reversible process can be calculated using the equation:

ΔH = ∫Cp dT

where Cp is the heat capacity at constant pressure and dT is the infinitesimal change in temperature.

If the process takes place at constant pressure (option A), then the heat transferred to the system is equal to the change in enthalpy. This is because the heat capacity at constant pressure (Cp) is defined as the amount of heat required to raise the temperature of the system by one degree Celsius at constant pressure. Therefore, the integral of Cp dT simplifies to Q.

On the other hand, if the process takes place at constant temperature (option B), volume (option C), or internal energy (option D), the heat transferred to the system is not equal to the change in enthalpy. In these cases, the work done on or by the system also contributes to the change in enthalpy.

To summarize, in a closed system, the change in enthalpy is equal to the heat transferred if the reversible process takes place at constant pressure. This is because the heat capacity at constant pressure represents the enthalpy change per unit temperature change at constant pressure.