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(B) The heat supplied at constant pressure is given by the formula: $\Delta Q = n C_P \Delta T$. Since nitrogen $(N_2)$ is a diatomic gas, its degrees

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$12$

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(B) The heat supplied at constant pressure is given by the formula: $\Delta Q = n C_P \Delta T$. Since nitrogen $(N_2)$ is a diatomic gas, its degrees of freedom $f = 5$. The molar heat capacity at constant pressure is $C_P = (\frac{f}{2} + 1) R = (\frac{5}{2} + 1) R = \frac{7}{2} R$. The number of moles $n = \frac{M}{M_0}$, where $M$ is the mass of the gas and $M_0$ is the molar mass $(28 \,g/mol)$. Substituting the values: $498 = (\frac{M}{28}) 	imes (\frac{7}{2}) 	imes 8.3 	imes 40$. Simplifying the equation: $498 = M 	imes (\frac{7}{56}) 	imes 8.3 	imes 40$. $498 = M 	imes 0.125 	imes 332$. $498 = M 	imes 41.5$. $M = \frac{498}{41.5} = 12 \,g$.

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