General Gas Equation

The various gas laws gives the relation between two properties while keeping the third property constant. In general practice all these three properties varies and it is required to have relation among all these properties. To do so Boyle’s law and Charles’s law are combined.

Let us consider a system which undergoes change of state from state 1 to state 2 by following Charles’s law and Boyle’s law simultaneously.

Fig. P-V diagram for general gas equation

For state change from 1 to 1’

V1/T1 = V1’/T1’ -------(1) (at const. Pressure)

For state change from 1’ to 2

P1’ V1’ = P2V2 -------(2) (at const. temp.)

V1’ = (P2V2)/ P1’ ------(3)

By inserting eq. (3) in eq. (1)

V1/T1 = (P2V2)/( P1’ T1’) -------(4)

From P-V diagram

P1’= P1

T1’ = T2

By inserting above values in eq. (4)

V1/T1 = (P2V2)/( P1 T2)

Or ( P1V1)­/T1 = (P2V2)/T­2 = CONSTANT

This equation is called General Gas Equation.