If $R$ is universal gas constant, the amount of heat needed to raise the temperature of $2 moles$ of an ideal monatomic gas from $273 K$ to $373 K$ when no work is done is 

As no work is done, therefore,  $∆W = 0$

According to first law of thermodynamics 

       $∆Q = ∆U + ∆∆W = ∆U = n{C}_V∆T = n\left(\frac{R}{\gamma -1}\right)∆T$

Here, $n = 2 , \gamma = \frac{5}{3}$

        $$\begin{gathered} ∆T = T_2-T_1 = \left(373-273\right) = 100 K \\ ∆Q = 2\times \frac{R}{\left({\displaystyle \frac{5}{3}}-1\right)}\times 100 = 300R \end{gathered}$$