Isothermal Process - Calculation of Work

Calculation of Work

In thermodynamics, the work involved when a gas changes from state A to state B is simply

For an isothermal, reversible process, this integral equals the area under the relevant pressure-volume isotherm, and is indicated in blue in the figure (at the bottom right-hand of the page) for an ideal gas. Again, p = nRT / V applies and with T being constant (as this is an isothermal process), we have:

By convention, work is defined as the work the system does on its environment. If, for example, the system expands by a piston moving in the direction of force applied by the internal pressure of a gas, then the work is counted as positive, and as this work is done by using internal energy of the system, the result is that the internal energy decreases. Conversely, if the environment does work on the system so that its internal energy increases, the work is counted as negative.

It is also worth noting that, for many systems, if the temperature is held constant, the internal energy of the system also is constant, and so . From First Law of Thermodynamics, so it follows that for this same isothermal process.

When no heat flows into or out of the gas because the temperature is constant, then there is no work done. Thus, work=0 which means external pressure is zero. This is called free expansion.