The constant pressure molar heat capacity of nitrogen gas, N₂, is 29.125 J K^-1 mol^-1 at 298.15 K. Calculate the change in the internal energy when 2.00 mol of nitrogen gas is heated so that its temperature increases by 25.0°C. Assume that the value of the heat capacity does not vary with temperature.

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Quizplus · Accepted Answer

The change in internal energy for an ideal gas at constant volume can be calculated using the formula ΔU = nCvΔT, where n is the number of moles, Cv is the molar heat capacity at constant volume, and ΔT is the change in temperature. For an ideal diatomic gas like nitrogen, Cv = Cp - R, where Cp is the molar heat capacity at constant pressure and R is the ideal gas constant (8.314 J/(mol·K)). Given Cp = 29.125 J/(mol·K) for nitrogen, Cv = 29.125 J/(mol·K) - 8.314 J/(mol·K) = 20.811 J/(mol·K). With n = 2.00 mol and ΔT = 25.0°C = 25.0 K, ΔU = 2.00 mol * 20.811 J/(mol·K) * 25.0 K = 1045.55 J, which is approximately 1.04 kJ.

The Constant Pressure Molar Heat Capacity of Nitrogen Gas, N2

The Constant Pressure Molar Heat Capacity of Nitrogen Gas, N₂