Exam #1 Review Trivial Concepts

1. Exam #1 Review TrivialConcepts

2. True or False (in the context of Thermodynamics) Every gaseous equation of state predicts a critical point

3. True or False (in the context of Thermodynamics) Every real gas has a critical point

4. True or False (in the context of Thermodynamics) The critical point represents a minimum in the compressibility factor, Z

5. True or False (in the context of Thermodynamics) The critical temperature is the highest temperature in which the substance may be a fluid

6. True or False (in the context of Thermodynamics) The sum of the heat and the work in a change in state is independent of path, but the difference is not independent of path

7. True or False (in the context of Thermodynamics) An isobaric, adiabatic expansion of an ideal gas cannot be reversible

8. True or False (in the context of Thermodynamics) An isobaric expansion of an ideal gas cannot be reversible

9. True or False (in the context of Thermodynamics) The function (pV/RT – A) has an exact differential

10. True or False (in the context of Thermodynamics) Adiabatic compression of any gas increases the internal energy of the gas

11. True or False (in the context of Thermodynamics) The Otto engine is used in automobiles because it has a greater efficiency than that of a Carnot engine

12. True or False (in the context of Thermodynamics) The state variable that indicates the direction of spontaneous change for an isolated system is G

13. True or False (in the context of Thermodynamics) If a gas is compressed reversibly and isentropically, the temperature must increase

14. True or False (in the context of Thermodynamics) If a gas is expanded inenthalpically the temperature must decrease

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18. 1. From the equation (∂U/∂V)T = T(∂p/∂T)V -p, show that (∂U/∂V)T = 0 for a gas that has the equation of state pV = RT

19. 1. From the equation (∂U/∂V)T = T(∂p/∂T)V -p, show that (∂U/∂V)T = 0 for a gas that has the equation of state pV = RT

20. 2. Since CV = (∂U/∂T)V by definition, one sometimes writes dU = CV dT. Under what circumstances is this true?

21. 2. Since CV = (∂U/∂T)V by definition, one sometimes writes dU = CV dT. Under what circumstances is this true?

22. 3. One mole of an ideal monoatomic gas is put through the reversible cycle shown below. Find the work, heat, change in Energy, and change in Enthalpy, for each stage and for the total cycle (1)-(2) Isochoric heating from 1.00 atm to 2.00 atm at 24.4 L (2)-(3) Isobaric cooling from 24.4 L to 12.2 L (3)-(1) Isothermal Expansion from 12.2L to 24.4 L State p, atm V, liters T, K (1) 1.00 24.4 298 (2) 2.00 24.4 596 (3) 2.00 12.2 298

27. 4. Prove that two reversible adiabatic paths can never cross. Assume that the energy of the system under consideration is a function of temperature only. (Hint Suppose that two such paths can intersect, and complete a cycle with the two paths plus one isothermal path. Consider the changes accompanying each stage of the cycle and show that they conflict with the Kelvin statement of the Second Law).

28. 4. Prove that two reversible adiabatic paths can never cross. Assume that the energy of the system under consideration is a function of temperature only. (Hint Suppose that two such paths can intersect, and complete a cycle with the two paths plus one isothermal path. Consider the changes accompanying each stage of the cycle and show that they conflict with the Kelvin statement of the Second Law).

29. 5. Represent the Carnot cycle on a temperature-entropy diagram and show that the area enclosed by the cycle is equal to the work done.

30. 5. Represent the Carnot cycle on a temperature-entropy diagram and show that the area enclosed by the cycle is equal to the work done.

32. Find an expression for the change in entropy when two blocks of the same substance and of equal mass, one at the temperature Thot and the other at Tcold are brought into thermal contact and allowed to reach equilibrium. Evaluate the change for two 500-g blocks of copper with Cp = 24.4 J /(K mol) and taking Thot = 500K and Tcold = 250 K

33. Find an expression for the change in entropy when two blocks of the same substance and of equal mass, one at the temperature Thot and the other at Tcold are brought into thermal contact and allowed to reach equilibrium. Evaluate the change for two 500-g blocks of copper with Cp = 24.4 J /(K mol) and taking Thot = 500K and Tcold = 250 K

35. 7. A gaseous sample consisting of 1.00 mol molecules is described by the equation of state pV = RT(1 + Bp). Initially at 373 K, it undergoes Joule-Thomson expansion from 100 atm to 1.00 atm. Given that Cp = 5/2R μ = 0.21 K atm-1 B = -0.525 (K/T) atm-1 and that these are constant over the temperature range involved, calculate ΔT for the gas.

36. 7. A gaseous sample consisting of 1.00 mol molecules is described by the equation of state pV = RT(1 + Bp). Initially at 373 K, it undergoes Joule-Thomson expansion from 100 atm to 1.00 atm. Given that Cp = 5/2R μ = 0.21 K atm-1 B = -0.525 (K/T) atm-1 and that these are constant over the temperature range involved, calculate ΔT for the gas.

37. 8. The cycle involved in the operation of a conventional internal combustion engine is called the Otto cycle. Air can be considered to be the working substance (i.e. CV = 5/2R ) and is assumed to be a perfect gas. The cycle consists of the following steps: I (A)-(B) Reversible adiabatic compression II (B)-(C) Reversible constant-volume pressure increase due to the combustion of a small amount of fuel; III (C)-(D) Reversible adiabatic expansion IV (D)-(A) Reversible and constant-volume pressure decrease Determine the change in entropy (of the system and of the surroundings) for each step of the cycle and determine an expression for the efficiency of the cycle, assuming that the heat is supplied in step II. Evaluate the efficiency for a compression ratio of 10:1. Assume that in state (A): V = 4.00L, p = 1.00 atm, and T = 300 K.