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(B) The internal energy $U$ of an ideal gas is given by $U = \mu C_V T$,where $\mu$ is the number of moles,$C_V$ is the molar heat capacity at constan

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$56 \, kg$ of nitrogen at $10^7 \, N/m^2$ and $300 \, K$

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(B) The internal energy $U$ of an ideal gas is given by $U = \mu C_V T$,where $\mu$ is the number of moles,$C_V$ is the molar heat capacity at constant volume,and $T$ is the absolute temperature.For monoatomic gases (He,Ar),$C_V = \frac{3}{2}R$. For diatomic gases $(N_2, O_2)$,$C_V = \frac{5}{2}R$.$A$: $\mu = 2$,$C_V = 1.5R$,$T = 300 \, K$. $U_A = 2 	imes 1.5R 	imes 300 = 900R$.$B$: $m = 56 \, kg = 56000 \, g$. Molar mass of $N_2 = 28 \, g/mol$. $\mu = \frac{56000}{28} = 2000 \, moles$. $C_V = 2.5R$,$T = 300 \, K$. $U_B = 2000 	imes 2.5R 	imes 300 = 1,500,000R$.$C$: $m = 8 \, g$. Molar mass of $O_2 = 32 \, g/mol$. $\mu = \frac{8}{32} = 0.25 \, moles$. $C_V = 2.5R$,$T = 300 \, K$. $U_C = 0.25 	imes 2.5R 	imes 300 = 187.5R$.$D$: $N = 6 	imes 10^{26}$ molecules. $\mu = \frac{N}{N_A} = \frac{6 	imes 10^{26}}{6 	imes 10^{23}} = 1000 \, moles$. $C_V = 1.5R$,$T = 900 \, K$. $U_D = 1000 	imes 1.5R 	imes 900 = 1,350,000R$.Comparing the values,$U_B$ is the largest.

Which one of the following gases possesses the largest internal energy?

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