(a) Show that internal energy of an ideal gas is expressed as
`U=(PV)/((gamma-1))` when `P=`pressure, `V=`volume and `gamma=(C_P)/(C_V)`.
(b) Hence find the internal energy of air in a room of volum `50m^3` at atmospheric pressure.
`(1Atm=10^5(N)/(m^2))`

Explanation

(a) Internal energy of `n` moles of an ideal gas at temperature `T` kelving is given by
`U=nC_(V)T=(nRT)/(gamma-1)=(PV)/(gamma-1)`
(b) For air (a diatomic gas) `gamma=1.4`
`U=(PV)/(gamma-1)=(10^5xx50)/(1.4-1)=(50xx10^5)/(0.4)`
`=1.25xx10^7J`