A monoatomic gas performs a work of (Q)/(4) where Q is the heat...

Using first law of thermodynamics,

$Q = ∆ U + W$

$⇒ Q = \DeltaU + \dfrac{Q}{4}$

$⇒ \DeltaU = \dfrac{3Q}{4}$

$⇒ ∆ U = \dfrac{3}{2}nR\DeltaT = \dfrac{3Q}{4}$

Therefore, molar heat capacity, $C = \dfrac{Q}{n ∆ T}$

$⇒ C = 2R$