Mathematical statement of the First law of Thermodynamics is
∆U = q + w
Case 1:
For a cyclic process involving isothermal expansion of an ideal gas
∆U = 0
∴ q = -w
In other words, during a cyclic process, the amount of heat absorbed by the system is equal to work done by the system.
Case 2:
For an isochoric process (no change in volume) there is no work of expansion.
∆V = 0
w = 0
∆U = 0
In other words, during isochoric process, the amount of heat supplied to the system is converted to its internal energy.
Case 3:
For an adiabatic process there is no change in heat .
i.e., q O.
Hence, q = 0
∆U = w
In other words, in an adiabatic process, the decrease in internal energy is exactly equal to the work done by the system on its surroundings.
Case 4:
For an isobaric process. There is no change in the pressure. P remains constant.
Hence, ∆U = q + w
∆U = q – P∆V
In other words, in an isobaric process a part of heat absorbed by the system is used for PV expansion work and the remaining is added to the internal energy of the system.
