Import Question JSON

$\text{Hint: } U = nC_V T = n \left(\frac{f}{2}\right) RT$ $\text{Step 1: Find the internal energy of 2 moles of helium at 300 K.}$ $\text{For monoatomic gas } \left(C_V = \frac{3}{2} R\right)$ $U = nC_V \Delta T$ $\Rightarrow U = 2 \times \frac{3}{2} R \times 300 = 900R \text{ J}$ $\text{Step 2: Find the internal energy of 56 kg of nitrogen at } 10^5 \text{ Nm}^{-2} \text{ and 300 K.}$ $\text{The molar mass of nitrogen } (\text{N}_2) = 28 \text{ gm/mol}$ $\text{The number of moles in the gas is given by;}$ $n = \frac{56,000 \text{ g}}{28 \text{ g/mol}} = 2000 \text{ mol}$ $\text{For diatomic gas } \left(C_V = \frac{5}{2} R\right)$ $U = nC_V \Delta T$ $\Rightarrow U = 2000 \times \frac{5}{2} R \times 300 = 1500 \times 10^3 R \text{ J}$ $\text{Step 3: Find the internal energy of 8 grams of oxygen at 8 atm and 300 K.}$ $\text{The molar mass of oxygen } (\text{O}_2) = 32 \text{ gm/mol}$ $\text{The number of moles in 8 grams of oxygen is given by;}$ $n = \frac{8 \text{ g}}{32 \text{ g/mol}} = 0.25 \text{ mol}$ $\text{For diatomic gas } \left(C_V = \frac{5}{2} R\right)$ $U = nC_V \Delta T$ $\Rightarrow U = 0.25 \times \frac{5}{2} R \times 300 = 187.5R \text{ J}$ $\text{Step 4: Find the internal energy of } 6 \times 10^{26} \text{ molecules of argon occupying 40 m}^3 \text{ at 900 K.}$ $1 \text{ mol} = 6.022 \times 10^{23} \text{ molecules}$ $\text{For Monoatomic gas } \left(C_V = \frac{3}{2} R\right)$ $\text{The number of moles in argon gas is given by;}$ $n = \frac{6 \times 10^{26}}{6.022 \times 10^{23}} \approx 10^3 \text{ mol}$ $U = nC_V \Delta T$ $\Rightarrow U = 10^3 \times \frac{3}{2} R \times 900 = 1350 \times 10^3 R \text{ J}$ $\text{Therefore, the gas with the largest internal energy is 56 kg of nitrogen at } 10^5 \text{ Nm}^{-2} \text{ and 300 K.}$ $\text{Hence, option (2) is the correct answer.}$