First Law

The First Law of Thermodynamics is just the law of energy conservation. This concept is easy to accept at the present time, but that was not always the case. The first scientist to mention the concept of total energy conservation was Mayer in 1842. As we already discussed in the mechanical equivalent of heat, his work was largely ignored at first. However, about five years later Hermann von Helmholtz and James Joule independently rediscovered this central principle of physics.

For a system that exchanges energy with its surroundings by means of work, W, or heat, Q, the change in internal energy, U, is:

$\Delta$U = Q - W

If Q > 0, then heat is added to the system, and if Q < 0, then heat is removed from the system. If W > 0, then work is done by the system, and if W < 0, then work is done on the system.

Sometimes one also finds another formulation of the first law of thermodynamics. If the energy changes are infinitesimally small, then one can write:

dU = dQ - dW

The first law finds important applications in special cases in which one of the thermodynamic variables is kept constant:

Isobaric Process (constant pressure)
Isometric Process (constant volume)
Isothermal Process (constant temperature), and
Adiabatic Process (no heat transfer, Q = 0).

We will study the processes above for an ideal gas.