The isothermal expansion of gases

To find the work done during the isothermal expansion of a gas, that is, the work done when the gas changes its volume, by expansion or compression, at a constant temperature. A contraction may be regarded as a negative expansion. There are three interesting applications. 

—The gas obeys Boyle s law, pv = constant, say, c. We have seen that the work done when a gas expands against any external pressure is represented by the product of the pressure into the change of volume. The work performed during any small change of volume, is 

Equations (3) and (4) play a most important part in the theory of gases, in thermodynamics and in the theory of solutions. The value of c is equal to the product of the initial volume, vlt and pressure, pv of the gas. Hence we may also put 

This equation has occupied a prominent place in the development of van der Waals theories of the constitution of gases and liquids. 

Example.—Find the work done when two litres of oarbon dioxide are compressed isothermally to one litre given van der Waals a = 0 00874 b = 0 0028 c = 0 00369. Substitute in (5), using a negative sign for contraction. 

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