Starting with the relation P = -(A/V), show that P = kBT(à In Q/V). Using argon as an example of an ideal monatomic gas, derive the ideal-gas equation (PV = nRT).Step 1 of 7Give the equation for the Helmholtz energy, A. (Use the following as necessary: S, T, and U.)A = U-TSU-TSGive the equation for entropy that contains the canonical partition function, Q. (Use the following as necessary: E, KB, Q, and T.)S =kpln(Q) +ETkB ln (Q) +FRStep 2 of 7We only need to consider the translationaltranslational 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 U₁.)A = -Tkaln(Q) + U₁0U₁ - kBT ln(Q)Step 3 of 7Substitute 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 =-(SA),.- (a In(@)); *kpT=BКВТStep 4 of 7For an ideal monatomic gas, the following is true. (Use the following as necessary: T, U, and V.)(3V) ₁ =T

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For an ideal monatomic gas, the following is true. (Use the following as necessary: T, U, and V.) T

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

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Starting with the relation P = -(A/V), show that P = kBT(à In Q/V). Using argon as an example of an ideal monatomic gas, derive the ideal-gas equation (PV = nRT).
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.)
S =
kpln(Q) +
E
T
kB ln (Q) +
FR
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 U₁.)
A = -Tkaln(Q) + U₁
0
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 =
-(SA),
.
- (a In(@)); *
kpT
=
B
КВТ
Step 4 of 7
For an ideal monatomic gas, the following is true. (Use the following as necessary: T, U, and V.)
(3V) ₁ =
T

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