The First Law

We have discussed the Zeroth and Second Laws. What is the First law? The first law of thermodynamics is actually a statement of the conservation of energy. The experiments of Benjamin Thompson, James Joule and others demonstrated that heat was a form of energy and that it could be produced by doing mechanical work, and also conversely could be transformed into mechanical energy. Let $dQ$ be the net amount of heat absorbed by a system in an infinitesimal transformation and $dW$ the amount of work done by the system (note the sign conventions!). Then the first law states that the quantity $dU$ defined by

$$dU = dQ - dW$$ (4.15)

is the same for all transformations that lead the system from its initial to final state, that is $\int dU$ is independent of the path of integration in state space and only depends on the end points. This property is not true individually of $dQ$ and $dW$ since the amount of heat absorbed or the work done depends also on the actual process, that is, path in state space. The quantity $U$ is called the internal energy of the system (Recall its appearance in the ideal gas law (4.10) derived using kinetic theory).