The enthalpy H is defined as

       

H = U + PV,

 

where U is the internal energy, P the pressure, and V the volume.  If we add heat to a system at constant pressure, the heat (energy) is equal to the increase of internal energy, U, plus the work done by the expansion of the gas, PV.

 

The equation for ideal gases is PV = nRT. If P is constant, which is the case for a fire in the room, the hot air causes the volume to increase. The work is PV. That is, enthalpy is the energy we have to add to a gas at constant pressure.