Enthalpy:- The heat content of a system at constant pressure is called enthalpy.

Let a system undergo a change from state A to state B by absorbing q calories of heat from the surroundings at a constant pressure P. In such a case change of volume will take place.

Let V_A be the volume of the system in state A and V_B is the volume of the system in state B. The work done by the system is given by equation.

W = p(V_B - V_A)

Substitute the value of W

ΔE = q - p(V_B - V_A)    ....(i)

But ΔE = E_B - E_A

∴ E_B - E_A = q - p(V_B - V_A)   ...(ii)

or, E_B - E_A = q - pV_B + pV_A

or, (E_B + pV_B) - (E_A - pV_A) = q   ...(iii)

The quantity E + pV is representing the total energy stored in a system and is called heat constant or enthalpy of a system. It is denoted by the symbol H

∴ H = E + pV   ...(iv)

E is definite quantity and is determined by the state of the system, p and V are also definite quantities. Therefore the quantity E + pV, i.e., H(enthalpy) is also a definite quantity and is determined by the state of the system.

It is neither possible nor it is required to determine the absolute value of enthalpy of a system. Only the change in enthalpy of the system which takes place due to change in any of the variable of the system is required and can be measured accurately.

For a system A, H_A = E_A + pV_A  ...(v)

For a system B, H_B = E_B + pV_B ...(vi)

Subtracting (vi) from (v),

H_B - H_A = (E_B - E_A) + p(V_B - V_A) ..(vii)

∴ ΔH = ΔE + PΔV  ....(viii)

ΔH represents the increase in that heat content of the system. Like ΔE it is also a definite property and depends on the initial and final state of the system. We can write Q = ΔE + pΔV

Enthalpy changes at constant value. When the volume is kept constant

ΔV = 0

pΔV = 0

∴ ΔH = ΔE

i.e., at constant volume the change in enthalpy is equal to the change in the internal energy.

Enthalpy changes at constant pressure. For a change at constant pressure, the enthalpy change equals the heat absorbed by the substance. Since for a monoatomic gas, all the internal energy is accounted for by the kinetic energy of its molecules, we can estimate enthalpy H, per mole of such a gas at a temperature T as

H = \(\frac{3}{2}\)RT + pV

= \(\frac{3}{2}\)RT + RT = \(\frac{5}{2}\)RT  [Since pV = RT]