The heat energy of $$743J$$ is needed to raise the temperature of $$5$$ moles of an ideal gas by $$2K$$ at constant pressure. How much heat energy is needed to raise the temperature of the same mass of the gas by $$2K$$ at constant volume?
Correct option is C. $$660J$$
as we know,
$$(Q)_P=nC_PΔT=\Delta H$$
$$C_P−C_V=R⇒C_V=C_P−R,\ (Q)_V=nC_VΔT=\Delta U$$
At constant pressure,
$$\Delta H=nC_PΔT=743J$$
At constant volume,
$$\Delta U=nC_vΔT=n(C_p−R)\Delta T=nC_PΔT-nRΔT$$
$$\Delta U=743−(5×8.3×2)$$
$$\Delta U=660J$$
Option C is correct.