One mole of an ideal monatomic gas undergoes a process described by the equation PV³=constant. The heat capacity of the gas during this process is:

PVγ=constant (Polytropic process)
Heat capacity in polytropic process is given by
[C = CV + R/(1-x)]
Given that PV³=constant ⇒ x=3. (1)
Also gas is monoatomic so CV=3/2R.. (2)
By formula C = (3/2)R + R/(1-3) = (3/2)R - R/2 = R
Hence, option A is correct