Should the internal energy of a system necessarily increase if heat is added to it?
No, the internal energy of the system necessarily should not increase if heat is added to it.
Explanation
1. Internal energy is defined as the sum of the kinetic energy and potential energy of molecules of the system. It includes only the energy associated with the random motion of molecules of the system.
2. Random motion of molecules is associated with the temperature of the system. Thus, any change in temperature will change the internal energy of the system.
3. Change in internal energy is given as
ΔU=Cv ΔT
Where ΔU= change in internal energy
Cv=molar specific heat at constant volume
ΔT= change in temperature.
4. If ΔT =0 then, ΔU will also be zero.
5. In the isothermal process, where the change in temperature is zero, ΔU is also zero.
6. According to First law of thermodynamics,
ΔQ=ΔU+ΔW
Where ΔQ=heat supplied to the system
ΔU=change in internal energy
ΔW=work done by the system
7. Since for an isothermal process ΔT=0, therefore ΔU=0. So, from the first law of thermodynamics ΔQ=ΔW.
8. For an isothermal process, heat supplied to the system is used up entirely in doing work.