## Alternative Formulation of the Second Law of Thermodynamics

The thermodynamic state of a substance is defined by the quantities – volume, – pressure, – Temperature and – internal energy.

These four quanties are related by the equations and one equation for the internal energy eg This means we can choose any two of these quantities as independent andf express the other two – dependent – variables in terms of the independent variables.

The second law of thermodynamics can be written (1) where and are independent.

Or as where and are independent (2)

Or as where and are independent (3)

Or as where and are independent (4)

Or as where U and p are independent (5)

Or as where and are independent. (6)

To show (1) write Then (7)

Now let Then (8)

Hence and Equate this expression with and from (7) to give and Hence we can write (1) as or he proof for (3) is similar.

To prove (4) take and as independent, then Then Rearrange the second of these to give Substitute into the first to give Compare these two equations with equations (7) to give and Substitute these into (1) to obtain (5) and (6) can be similarly proved. 