Tutorial 6 2015
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THE UNIVERSITY OF ZAMBIA Department of Physics P3242 Statistical and Thermal Physics Tutorial #6 1. An ideal gas has a temperature-independent molar heat capacity c v at constant volume. Let γ = c p /c v denote the ratio of its specific heats. The gas is thermally insulated and is allowed to expand quasi-statically from an initial volume V i at temperature T i to a final volume V f . a) Use the relation pV γ =constant to find the final temperature T f of this gas. b) Use the fact that the entropy remains constant in this process to find the final temperature T f . 2. Problem 5.2 on p 192 of Reif. 3. Problem 5.3 on p 193 of Reif. 4. Liquid mercury at atmospheric pressure and 0 0 C has a molar volume of 14.72 cc/mole and a specific heat at constant pressure of c p = 28.0 J/mole.K. Its coefficient of expansion is α = 1.81 × 10 4 K -1 and its compressibility is κ = 3.88 × 10 -12 cc/dyne. Find its specific heat c v at constant volume and the ratio γ ≡ c p /c v . 5. Prove that as T → 0, c v → 0. 6. Show that in the free expansion of an ideal gas, the internal energy is conserved. 7. Show that when a van der Waals gas undergoes a free expansion, the temperature drop is T 2 - T 1 = - a c v ( 1 v 1 - 1 v 2 ), where v 1 is the initial molar volume and v 2 the final. 8. Show that in the throttling (Joule-Thomson) process, the enthalpy is conserved. 9. Explain the importance of Carnot engines and describe the operation of one. 1
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Transcript of Tutorial 6 2015
THE UNIVERSITY OF ZAMBIADepartment of Physics
P3242Statistical and Thermal Physics
Tutorial #6
1. An ideal gas has a temperature-independent molar heat capacity cv at constant volume.Let γ = cp/cv denote the ratio of its specific heats. The gas is thermally insulated and isallowed to expand quasi-statically from an initial volume Vi at temperature Ti to a finalvolume Vf .
a) Use the relation pV γ =constant to find the final temperature Tf of this gas.
b) Use the fact that the entropy remains constant in this process to find the finaltemperature Tf .
2. Problem 5.2 on p 192 of Reif.
3. Problem 5.3 on p 193 of Reif.
4. Liquid mercury at atmospheric pressure and 00C has a molar volume of 14.72 cc/moleand a specific heat at constant pressure of cp = 28.0 J/mole.K. Its coefficient ofexpansion is α = 1.81× 104K−1 and its compressibility is κ = 3.88× 10−12cc/dyne.Find its specific heat cv at constant volume and the ratio γ ≡ cp/cv.
5. Prove that as T → 0, cv→ 0.
6. Show that in the free expansion of an ideal gas, the internal energy is conserved.
7. Show that when a van der Waals gas undergoes a free expansion, the temperature dropis
T2−T1 =−acv(
1v1− 1
v2),
where v1 is the initial molar volume and v2 the final.
8. Show that in the throttling (Joule-Thomson) process, the enthalpy is conserved.
9. Explain the importance of Carnot engines and describe the operation of one.
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