(3) Partition function of an ideal gas comprising N particles of mass m in a volume V, which is in equilibrium with a heat bath at temperature T (or B = 1/kT), was calculated in lecture as: VN Z = (2πmkT) 3 N/2 VN 3N/2 m N!h3N N! (2nh?ß, using the integral f e-cx2 Now consider an ideal gas comprising N particles of two-atom molecule of mass m. Kinetic energy is separated as E = Etransl + Erot, Wwhere 1 Etransl 1 1 (Pi + p3 + p?); Erot =7(Pổ + P),0soST,0s PS 2n. (på + ),0 < 0 < T,0 < p< 2n. 2m 21 sin? 0 (a) Calculate the partition function for ideal gas comprising two-atom molecules. (b) Calculate the heat capacity.

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(3) Partition function of an ideal gas comprising N particles of mass m in a volume V, which is in
equilibrium with a heat bath at temperature T (or Bß = 1/kT), was calculated in lecture as:
%3D
3N/2
VN
(2nmkT)³N/2
VN
m
Z =
N!h3N
N! (2nh?ß,
using the integral
e-cx2
Now consider an ideal gas comprising N particles of two-atom molecule of mass m. Kinetic energy
is separated as E = Etransl + Erot; where
1
1
Etransl =
2m
-(P를 +pg + p2); Erot
(på +
p),0 <θ< T,0<Φ< 2π.
21
sin? 0
(a) Calculate the partition function for ideal gas comprising two-atom molecules.
(b) Calculate the heat capacity.
Transcribed Image Text:(3) Partition function of an ideal gas comprising N particles of mass m in a volume V, which is in equilibrium with a heat bath at temperature T (or Bß = 1/kT), was calculated in lecture as: %3D 3N/2 VN (2nmkT)³N/2 VN m Z = N!h3N N! (2nh?ß, using the integral e-cx2 Now consider an ideal gas comprising N particles of two-atom molecule of mass m. Kinetic energy is separated as E = Etransl + Erot; where 1 1 Etransl = 2m -(P를 +pg + p2); Erot (på + p),0 <θ< T,0<Φ< 2π. 21 sin? 0 (a) Calculate the partition function for ideal gas comprising two-atom molecules. (b) Calculate the heat capacity.
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