Step 5 of 7 Give the equation for the canonical partition function Q. Remember that only the translational partition function needs to be considered for an ideal monatomic gas. (Use the following as necessary: e, h, kg, m, N, T, T, and V.) Q=
Step 5 of 7 Give the equation for the canonical partition function Q. Remember that only the translational partition function needs to be considered for an ideal monatomic gas. (Use the following as necessary: e, h, kg, m, N, T, T, and V.) Q=
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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Question
![Give the equation for the Helmholtz energy, A. (Use the following as necessary: S, T, and U.)
A = U-TS
- TS
Give the equation for entropy that contains the canonical partition function, Q. (Use the following as necessary: E, kB, Q, and T.)
E
E
S = k ln(Q) +
B
kB ln (Q) +
Step 2 of 7
We only need to consider the translational
translational partition function for an ideal monatomic gas, so E = U - Uo.
Combine this equation with the equations for S and A from Step 1. (Use the following as necessary: KB, Q, T, U, and Up.)
A =
|— Tkôln(Q) + U
U₁ - KBT ln(Q)
Step 3 of 7
Substitute the equation from Step 2 into the given equation for P and complete the partial derivative. (Use the following as necessary: kB, Q, T, U, and Up.)
-(SA),
P = -
a In(Q)). KBT
=
KBT
Step 4 of 7
For an ideal monatomic gas, the following is true. (Use the following as necessary: T, U, and V.)
(U) = UT
-
0
Step 5 of 7
Give the equation for the canonical partition function Q. Remember that only the translational partition function needs to be considered for an ideal monatomic gas. (Use the following as necessary:
e, h, kB, m, N, T, T, and V.)
Q =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F048c94c5-7ffa-4d93-8586-3256b3e2fe08%2F32f231a0-b100-451e-9081-2746253a8ca6%2Fc3y77d_processed.png&w=3840&q=75)
Transcribed Image Text:Give the equation for the Helmholtz energy, A. (Use the following as necessary: S, T, and U.)
A = U-TS
- TS
Give the equation for entropy that contains the canonical partition function, Q. (Use the following as necessary: E, kB, Q, and T.)
E
E
S = k ln(Q) +
B
kB ln (Q) +
Step 2 of 7
We only need to consider the translational
translational partition function for an ideal monatomic gas, so E = U - Uo.
Combine this equation with the equations for S and A from Step 1. (Use the following as necessary: KB, Q, T, U, and Up.)
A =
|— Tkôln(Q) + U
U₁ - KBT ln(Q)
Step 3 of 7
Substitute the equation from Step 2 into the given equation for P and complete the partial derivative. (Use the following as necessary: kB, Q, T, U, and Up.)
-(SA),
P = -
a In(Q)). KBT
=
KBT
Step 4 of 7
For an ideal monatomic gas, the following is true. (Use the following as necessary: T, U, and V.)
(U) = UT
-
0
Step 5 of 7
Give the equation for the canonical partition function Q. Remember that only the translational partition function needs to be considered for an ideal monatomic gas. (Use the following as necessary:
e, h, kB, m, N, T, T, and V.)
Q =
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