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

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

Physical Chemistry
Physical Chemistry
2nd Edition
ISBN:9781133958437
Author:Ball, David W. (david Warren), BAER, Tomas
Publisher:Ball, David W. (david Warren), BAER, Tomas
Chapter2: The First Law Of Thermodynamics
Section: Chapter Questions
Problem 2.52E: Use the data in Table 2.2 to determine Hp T for Ar at 0C and 1atm. Make any reasonable assumptions...
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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
Transcribed Image Text: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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ISBN:
9781133958437
Author:
Ball, David W. (david Warren), BAER, Tomas
Publisher:
Wadsworth Cengage Learning,
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