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

Options

A. `2RT_(0)`
B. `RT_(0)`
C. `(3)/(2)RT_(0)`
D. `(1)/(2)RT_(0)`

Answer

A

Explanation

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)`