Heat energy of 743 J is needed to raise the temperature of 5 moles of an ideal gas by 2 K at constan

Question

Heat energy of 743 J is needed to raise the temperature of 5 moles of an ideal gas by 2 K at constant pressure. How much heat energy is needed to raise the temperature of the same mass of the gas by 2 K at constant volume? (R = 8.3 J/K-mol)

Accepted Answer

$\frac{q_{V}}{q_{P}} = \frac{n.C_{V,m}.\Delta T}{n.C_{P,m}.\Delta T} = \frac{1}{\gamma}$

$\Rightarrow q_{v} = \frac{1}{\left( \frac{74.3}{66} \right)} \times 793 = 660\text{ J} $$$\left( C_{P,m} = \frac{743}{5 \times 2} = 74.3 \Rightarrow C_{V,m} = 74.3 - 8.3 = 66.0 \right)$$

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