One mole of a monatomic ideal gas undergoes four thermodynamic...

Process - $I$ is an adiabatic process
$∆ Q = ∆ U + W$
$∆ Q = 0$
$W = - ∆ U$
Volume of gas is decreasing $⇒ W < 0$
$∆ U > 0$
$⇒$ Temperatuer of gas increases
$⇒$ No heat is exchanged between the gas and surrounding.
Process - $II$ is an isobaric process
(Pressure remain constant)
$W = P ∆ V = 3{P}_{0}\left[3{V}_{0} - {V}_{0}\right] = 6{P}_{0}{V}_{0}$
Process - $III$ is an isochoric process
(Volume remain constant)
$∆ Q = ∆ U + W$
$W = 0$
$∆ Q = ∆ U$
Process - $IV$ is an isothermal process
(Temperature remains constant)
$∆ Q = ∆ U + W$
$∆ U = 0$