# Internal energy equals to average kinectic energy ?

by Outrageous
Tags: average, energy, equals, internal, kinectic
 P: 375 For ideal gas , can I assume Cv dT = nkT (3/2) , thank you
HW Helper
P: 6,507
 Quote by Outrageous For ideal gas , can I assume Cv dT = nkT (3/2) , thank you
No. Molar heat capacity, Cv = 3R/2 only for ideal monatomic gases. You are also mixing temperature change with temperature here.

Using molar heat capacity 3R/2 for a monatomic ideal gas:

$\int_{Ti}^{Tf} nC_vdT = \frac{3}{2}nR(T_f - T_i) = \frac{3}{2}nR\Delta T = \frac{3}{2}Nk\Delta T$

AM
P: 375
 Quote by Andrew Mason No. Molar heat capacity, Cv = 3R/2 only for ideal monatomic gases. You are also mixing temperature change with temperature here. Using molar heat capacity 3R/2 for a monatomic ideal gas: $\int_{Ti}^{Tf} nC_vdT = \frac{3}{2}nR(T_f - T_i) = \frac{3}{2}nR\Delta T = \frac{3}{2}Nk\Delta T$ AM
Thanks for compact explanation.

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