`(1//2)` mole of helium is contained in a container at STP how much heat energy is needed to double the pressure of the gas, keeping the volume constant? Heat capacity of gas is `3 J g^(-1)K^(-1)`.

Explanation

Here, `n=1/2 C_(upsilon) = 3 Jg^(-1) K^(-1), M=4 :. C_(upsilon) = Mc_(upsilon) = 4 xx 3 = 12 J mole^(-1)K^(-1)`
At constant volume `P prop T :. (P_2)/(P_1) = (T_2)/(T_1) = 2, T_(2) = 2 T_(1)`
Rise in temperature `Delta T = T_(2) - T_(1) = 2T_(1)-T_(1) = T_(1) = 273 K`
Heat required , `Delta Q = n C_(upsilon) Delta T = 1/2 xx 12 xx 273 = 1638 J`.