One mole of oxygen is heated at constant pressure starting at `0^(@)C`. How much heat energy must be added to the gas to double its volume ?

Explanation

`Delta W = int_(V)^(2V) pdV = p_(0) V = RT_(0)`
`Delta U = int C_(v) dT = int_(V)^(2V) (R )/(gamma - 1) dT`
At constant pressure fixed at
`p_(0) dV = RdT ( :' pV = RT)`
`:. Delta U = (1)/(gamma -1) int_(V)^(2V) p_(0) dV = (p_(0)V)/(gamma -1) = (RT_(0))/(gamma -1)`
`:. Delta Q = Delta U + Delta W = (RT_(0))/(gamma - 1) + RT_(0) = (gamma RT_(0))/(gamma -1)`
Since oxygen is diatomic, `gamma = 1.4`
`:. Delta Q = (1.4 xx 8.3 xx 273)/(1.4 - 1) = 7931 J`