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 equationsand 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) whereandare independent.

Or aswhereandare independent (2)

Or aswhereandare independent (3)

Or aswhereandare independent (4)

Or aswhere U and p are independent (5)

Or aswhereandare independent. (6)

To show (1) write


Now let



Equate this expression withandfrom (7) to give


Hence we can write (1) asor

he proof for (3) is similar.

To prove (4) takeandas independent, then


Rearrange the second of these to give

Substitute into the first to give

Compare these two equations with equations (7) to give


Substitute these into (1) to obtain

(5) and (6) can be similarly proved.

Add comment

Security code