The heat supplied to one mole of an ideal monoatomic gas in increasing temperature from `T_(0)` to `2T_(0)` is `2RT_(0)`. Find the process to which the gas follows

Options

A. `P^(2)V^(-1) = constant`
B. `PV^(-1) = constant`
C. `P^(-1)V = constant`
D. `PV^(-1) = constant`

Answer

D

Explanation

The supplied to the gas, `Q = nC(DeltaT)`
`n` is the number of moles in our case `n=1`, and `C` is the molar heat capacity of the gas
For polytropic molar heat capacity is given by
`C = R/((gamma-1))+(R)/((1-N))`
`=R/((5//3)-1)+(R)/((1-N))= 3/2 R+(R)/((1-N))`
`Q = n[(3R)/(2)+(R)/(1-N)] (2T_(0)-T)`
`(1)RT_(0)[(5-3N)/(2(1-N))] = 2RT_(0)` (given)
or `5-3N=4(1-N)`
`or N=-1`
Hence equation of process , `PV^(-1)= consta nt`.