360equipartition

2 the constant pressure molar heat capacity can then

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Unformatted text preview: C v,m = ∂ ∂T 3 ( 2 RT ) 3 R. 2 The constant pressure molar heat capacity can then be obtained using the relation € C p,m = C v,m + R . For the monatomic gas, the result is € C p,m = C v,m + R = C p,m = 3R + 2 5 R. 2 R Substituting the value of R, the theoretical prediction for the constant pressure heat capacity of a monatomic gas is € C p,m = 5 2 R = 5 2 (8.314 J mol –1 –1 C p,m = 20.79 J mol K K –1 –1 ) . This matches the experimental values of the heat capacities of He and Ne reported in the table above. € Beyond m onatomic g ases For diatomic molecules along with linear and nonlinear polyatomic molecules in the gas phase, the number of degrees of freedom can be determined and therefore the theoretical internal energy and heat capacity can be predicted. In addition to the 3 translational degrees of freedom, contributions from rotational and vibrational...
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