One mole of an ideal monoatomic gas undergoes a process as shown in the figure. Find the molar specific heat of the gas in the process.

R is a gas constant.

Options

A. `(3R)/(4)`
B. `R/2`
C. `R/3`
D. `(2R)/(3)`

Answer

B

Explanation

`V=m(1/T), m` = slope of the curve
`VT = consta nt. TdV+VdT = 0` ..(i)
`dV =-V/T dT`
`Q = DeltaU+W`
`CdT=C_(V)dT + PdV(2)`
from (1) and (2)
`cdT = C_(V)dT-P/T VdT implies C =C_(V)-(PV)/(T)`
For monoatomic gas `C_V = 3/2 R`
`C = C_(V) - R = 3/2R-Rimplies C = R/2`