The constant pressure molar heat capacity, C_{p, m}C p, m , of nitrogen gas, N_2N 2 , is 29.125\text{ J K}^{-1}\text{ mol}^{-1}29.125 J K −1 mol −1 at 298\text{ K}298 K. Calculate the change in the internal energy when 20\text{ mol}20 mol of nitrogen gas at 298\text{ K}298 K is heated so that its temperature increases by 15.0^{\circ}\text{C}15.0 ∘ C. You may assume constant heat capacity over the temperature range.

Explanation:

Constant pressure molar heat capacity Cp = 29.125 J /K.mol

If Cv be constant volume molar heat capacity

Cp - Cv = R

Cv = Cp - R

= 29.125 - 8.314 J

= 20.811 J

change in internal energy = n x Cv x Δ T

n is number of moles , Cv is molar heat capacity at constant volume ,  Δ T is change in temperature

Putting the values

= 20 x 20.811 x 15

= 6243.3 J.

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