Substitute the equation from Step 2 into the given equation for P and complete the partial derivative. (Use the following as necessary: kg, Q, T, U, and Up.)P = --(3+),T- (ain(@)),КВТ=KBTStep 4 of 7For an ideal monatomic gas, the following is true. (Use the following as necessary: T, U, and V.)(3V)₁ = 1 UT0Step 5 of 7Give 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.)N(2πmkBT) VeNh³Q =(2µmkµT)h³vXStep 6 of 7Determine In(Q) using the equation for Q from Step 5. (Use the following as necessary: e, h, kB, M, N, π, T, and V.)VeIn(Q)NIn(2μmkBT)Nh³(2π m kBT) eN ln (V) + NlnNh³Substitute into the equation for P from Step 3 and solve the partial derivative. (Use the following as necessary: e, h, kg, m, N, π, T, and V.)NKBTP =V|KBTN-VStep 7 of 7Rearrange the equation for P from Step 6 to solve for PV. (Use the following as necessary: KB, N, and T.)PV =KBTNThe number of particles, N, and the Boltzmann constant, kB, can be given in terms of Avogadro's constant, NA. (Use the following as necessary: n, NA, and R.)PVN =КВТXPVKBTNXSubstitute these variables into the equation for PV and simplify. (Use the following as necessary: n, NA, R, and T.)PV = nRT

Step 4 To determine the value of dUdVT for Ideal monoatomic gas.

Answered: For an ideal monatomic gas, the…

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

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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Substitute the equation from Step 2 into the given equation for P and complete the partial derivative. (Use the following as necessary: kg, Q, T, U, and Up.)
P = -
-(3+),
T
- (ain(@)),
КВТ
=
KBT
Step 4 of 7
For an ideal monatomic gas, the following is true. (Use the following as necessary: T, U, and V.)
(3V)₁ = 1 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, kg, m, N, T, T, and V.)
N
(2πmkBT) Ve
Nh³
Q =
(2µmkµT)h³v
X
Step 6 of 7
Determine In(Q) using the equation for Q from Step 5. (Use the following as necessary: e, h, kB, M, N, π, T, and V.)
Ve
In(Q)
N
In
(2μmkBT)
Nh³
(2π m kBT) e
N ln (V) + Nln
Nh³
Substitute into the equation for P from Step 3 and solve the partial derivative. (Use the following as necessary: e, h, kg, m, N, π, T, and V.)
NKB
T
P =
V
|KBTN-
V
Step 7 of 7
Rearrange the equation for P from Step 6 to solve for PV. (Use the following as necessary: KB, N, and T.)
PV =
KBTN
The number of particles, N, and the Boltzmann constant, kB, can be given in terms of Avogadro's constant, NA. (Use the following as necessary: n, NA, and R.)
PV
N =
КВТ
X
PV
KB
TN
X
Substitute these variables into the equation for PV and simplify. (Use the following as necessary: n, NA, R, and T.)
PV = nRT

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