One mole of an ideal monatomic gas at temperature T_(0) expands slowly according to the law (P)/(V) = constant. If the final temperature is 2T_(0), heat supplied to the gas is

One mole of an ideal monatomic gas at temperature T_(0) expands slowly

1.	One mole of an ideal monatomic gas at temperature T_(0) expands slowly according to the law (P)/(V) = constant. If the final temperature is 2T_(0), heat supplied to the gas is
Answer» `2RT_(0)` `RT_(0)` `(3)/(2)RT_(0)` `(1)/(2)RT_(0)` Solution :In a PROCESS `PV^(x)` = constant, molar heat capacity is GIVEN by `C = (R )/(gamma - 1) + (R )/(1-x)` As the process is `(P)/(V)` = constant, i.e., `PV^(-1)` = constant, therefore, `x = -1` For a MONATOMIC GAS, `gamma = 5//3` `:. C = (R )/((5)/(3)-1) + (R )/(1-(-1)) = (3)/(2)R + (R )/(2) = 2R` Heat supplied to the gas is `Delta Q = nC(Delta T) = 1(2R)(2T_(0) - T_(0)) = 2RT_(0)`