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

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

Chemistry: Principles and Practice
Chemistry: Principles and Practice
3rd Edition
ISBN:9780534420123
Author:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward Mercer
Publisher:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward Mercer
Chapter5: Thermochemistry
Section: Chapter Questions
Problem 5.101QE: In the 1880s, Frederick Trouton noted that the enthalpy of vaporization of 1 mol pure liquid is...
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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
Transcribed Image Text: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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