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Question

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?

A
$$826J$$
B
$$743J$$
C
$$660J$$
D
$$600J$$
Solution
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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,

$$\Delta H=nC_P​ΔT=743J$$

At constant volume,

$$\Delta U=nC_v​ΔT=n(C_p​−R)\Delta T=nC_P​ΔT-nRΔT$$

$$\Delta U=743−(5×8.3×2)$$

$$\Delta U=660J$$

Option C is correct.

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