(i) The pressure and temperature of 0.8 g of He gas are 1 atm and 298 K respectively. If 400 J of heat is applied to the gas at constant volume, what will be change in internal energy and the final temperature of the gas ?
(ii) If the same amount of heat is applied to the gas at constant pressure, then what will be the change in internal energy and the final temperature of the gas ? For both the cases, assume He gas behaves ideally and its `C_(V)=(3)/(2)R`.

Explanation

(i) `q_(V)= Delta U= nC_(V)(T_(2)-T_(1))= ((0.8)/(4))xx(3)/(2)R(T_(2)-T_(1))`
[For a monoatomic gas like He, `C_(V)=(3)/(2)R]`
or `, 400 J= 0.2xx(3)/(2)xx8.314 (T_(2)-298)J`
`therefore T_(2)= 458.37 K`
So, `q_(V)= Delta U= 400 J`.
(ii) `q_(P)=Delta H= n C_(P)(T_(2)-T_(1))= 0.2xx(5)/(2)R(T_(2)-T_(1))`
[For a monoatomic gas like He, `C_(P)= (5)/(2)R]`
or, `400= 0.2xx(5)/(2)xx8.314 (T_(2)-298) J`
or, `T_(2)= 394.22 K therefore Delta H= q_(P)= 400 J `
`Delta U= Delta H- nR Delta T= 400-0.2xx8.314 (394.22-298)`
`= -240 J`