An isothermal process is a change of a system, in which the temperature remains constant. For an ideal gas during an isothermal expansion the enthalpy, as well as internal energy, remains constant. During isothermal expansion of an ideal gas, ∆E=0,∆T=0 From the definition of enthalpy, H=E+PV or ∆H=∆E+∆(PV) or ∆H=∆E+∆(nRT) \{ Since, PV=nRT for an ideal gas\} or ∆H=∆E+nR∆T or ∆H=0