For a mechanically reversible isobaric process taking place in a closed system involving $5$ moles of an ideal gas, the temperature increases from an initial value of $300 \: K$ to a final value of $450 \: K$. If the specific heat capacity at constant volume $\left(C_{\mathrm{v}}\right)$ is given as $12.5 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$ and gas constant is $8.314 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$, the amount of heat transferred to the system will be $\_\_\_\_\_$ $\mathrm{J}$.
(Round off to the nearest integer)
