Step 6 of 7 Determine In(Q) using the equation for Q from Step 5. (Use the following as necessary: e, h, kg, m, N, 7, T, and V.) In(Q) = Substitute into the equation for P from Step 3 and solve the partial derivative. (Use the following as necessary: e, h, kg, m, N, 7, T, and V.) P =
Step 6 of 7 Determine In(Q) using the equation for Q from Step 5. (Use the following as necessary: e, h, kg, m, N, 7, T, and V.) In(Q) = Substitute into the equation for P from Step 3 and solve the partial derivative. (Use the following as necessary: e, h, kg, m, N, 7, T, and V.) P =
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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
Transcribed Image Text:Step 1 of 7
Give the equation for the Helmholtz energy, A. (Use the following as necessary: S, T, and U.)
A = U-TS
U-TS
Give the equation for entropy that contains the canonical partition function, Q. (Use the following as necessary: E, kB, Q, and T.)
E
S = kaln(Q)+
E
T
kB ln (Q) +
4
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 = -Tk ln(Q) + U₁
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.)
P =
-(3x),
・ (a In (@)), · KB¹
KBT
Step 4 of 7
For an ideal monatomic gas, the following is true. (Use the following as necessary: T, U, and V.)
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, 7, T, and V.)
N
(2πmkBT) Ve
Nh³
Q =
(2µmkµT)h³v
Step 6 of 7
Determine In(Q) using the equation for Q from Step 5. (Use the following as necessary: e, h, kg, m, N, T, T, and V.)
In(Q) =
Substitute into the equation for P from Step 3 and solve the partial derivative. (Use the following as necessary: e, h, kB, M, N, π, T, and V.)
P =
(au ) ₁ =
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