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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 =

Physical Chemistry
Physical Chemistry
2nd Edition
ISBN:9781133958437
Author:Ball, David W. (david Warren), BAER, Tomas
Publisher:Ball, David W. (david Warren), BAER, Tomas
Chapter18: More Statistical Thermodynamics
Section: Chapter Questions
Problem 18.4E
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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 =
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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ISBN:
9781133958437
Author:
Ball, David W. (david Warren), BAER, Tomas
Publisher:
Wadsworth Cengage Learning,
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