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.

Question

Physics

Nico Leon

15 February, 09:01

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.

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Rambler · Answer 1

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.