First Law of Thermodynamics

 

The first law of thermodynamics is a statement of the law of conservation of energy applied to thermodynamic systems.

When a small amount of heat $dQ$ is supplied to a thermodynamic system, a part of it may be used to increase the internal energy of the system, while the remaining part may be used to do external work.

Thus,

$$\boxed{dQ=dU+dW}$$

where

• $dQ$ = infinitesimal amount of heat supplied to the system,
• $dU$ = infinitesimal change in internal energy,
• $dW$ = infinitesimal work done by the system.

If the system performs work $dW$ against an external pressure $P_{\rm ext}$,

$$\boxed{dW=P_{\rm ext}\,dV}$$

Therefore,

$$\boxed{dQ=dU+P_{\rm ext}\,dV}$$

For a quasi-static process, $P_{\rm ext}=P$, so

$$\boxed{dQ=dU+P\,dV}$$

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