AP PHYSICS 2 WHS-CH-15 Thermodynamics Show all your work, equations used, and box in your answers!

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1 AP PHYSICS 2 WHS-CH-15 Thermodynamics Show all your work, equations used, and box in your answers! Nicolas Léonard Sadi Carnot ( ) Sadi Carnot was a French military engineer and physicist, often described as the "father of thermodynamics". Multiple Choice 1. Through a series of thermodynamic processes, the internal energy of a sample of confined gas is increased by 560J. If the net amount of work done on the sample by its surroundings is 320J, how much heat was transferred between the gas and its environment? (A) 240 J absorbed (C) 880J absorbed (B) 240J dissipated (D) 880J dissipated 2. What s the total work performed on the gas as it s transferred from state a to state c, along the path indicated? (A) 1,500 J (B) 3,000 J (C) 4,500 J (D) 5,000 J During each cycle, a heat engine absorbs 400J of heat from its high-temperature source and discards 300J of heat into its low temperature sink. What is the efficiency of this engine? (A) 1/7 (B) ¼ (C) 3/7 (D) 4/7 (E) ¾ Of the following, which is the best description of the second law of thermodynamics? (A) The total energy of the universe is a constant (B) The efficiency of a heat engine can never be greater than 50 percent (C) The amount of heat required to vaporize a liquid is greater than the amount of heat required to melt a solid of the same substance (D) The entropy of the universe is always increasing 5. Which of the following is a true statement? (A) It is impossible to convert work entirely into heat (B) It is impossible to transfer heat from a cooler to a hotter body (C) The second law of thermodynamics is a consequence of the first law of thermodynamics (D) All of these statements are false 1

2 Which is an important feature of the Carnot cycle? (A) Efficiency is determined only by the properties of the working substance used (B) It is the most efficient engine operating between two temperatures (C) Efficiency can be 100% (D) Efficiency depends only on the absolute temperature of the hot reservoir used According to the laws of thermodynamics (A) heat energy cannot be completely converted into mechanical energy (B) heat flows naturally from a region of lower to a region of higher temperature (C) mechanical energy cannot be completely converted into heat (D) entropy of a system approaches zero as the temperature approaches absolute zero A Carnot engine operating between a reservoir of liquid mercury at its melting point and a colder reservoir extracts 18 J of heat from the mercury and does 5 J of work during each cycle. What is the temperature of the colder reservoir? (Use melting temperature of mercury = 233 K) (A) 168 K (C) 57 K (B) 66 K (D) 82 K When 0.75 kg of water at 0 o C freezes, what is the change in entropy of the water? (Use latent heat of fusion of water Lf = 33,400 J/kg) (A) 92J/K (C) 44 J/K (B) 18 J/K (D) 80 J/K The graph shows a PV diagram for 5.1 g of oxygen gas in a sealed container. The temperature of T1 is 20 o C. What are the values for temperatures of T3 and T4 respectively? (Use the gas constant R = J/mol.K) (A) 53 o C and 387 o C (B) 14 o C and 34 o C (C) 210 o C and 640 o C (D) 12 o C and 58 o C 11. What is the term for a process when a gas is allowed to expand as heat is added to it at constant pressure? (A) Isochoric (C) Adiabatic (B) Isobaric (D) Isothermal 12. A Carnot engine is used as an air conditioner to cool a house in the summer. The air conditioner removes 20 kj of heat per second from the house, and maintains the inside temperature at 293 K, while the outside temperature is 307 K. What is the power required for the air conditioner? (A) 2.3 kw (C) 1.6 kw (B) 3.22 kw (D) 0.96kW 2

3 The figure shows mol of gas that undergoes the process What is the volume of V3? (Use ideal gas constant R = J/mol.K and 1 atm = 101,325 Pa) (A) 435 cm 3 (B) 568 cm 3 (C) 656 cm 3 (D) 800 cm 3 When a gas expands adiabatically: (A) it does no work (B) work is done on the gas (C) the internal (thermal) energy of the gas decreases (D) the internal (thermal) energy of the gas increases An ideal gas is compressed via an isobaric process to one-third of its initial volume. Compared to the initial pressure, the resulting pressure is: (A) more than three times greater (C) three times greater (B) nine times greater (D) the same 16. A solid sample of a pure compound is contained in a closed, well-insulated container. Heat is added at a constant rate and the sample temperature is recorded. The resulting data is shown in the graph. Which of the following statements is true? (A) After 5 minutes, the sample was a mixture of solid and liquid (B) The heat capacity of the solid phase is greater than that of the liquid phase (C) The sample never boiled (D) The heat of fusion is greater than the heat of vaporization When the first law of thermodynamics, Q = ΔU + W, is applied to an ideal gas that is taken through an adiabatic process: (A) Q = 0 (B) W > ΔU (C) ΔU = 0 (D) W = 0 A heat pump pumps heat into a greenhouse at a rate of 50 kw. If work is being done to run this heat pump at a rate of 7.5 kw, what is the coefficient of performance of the heat pump? (A) 0.9 (B) 1.7 (C) 3.1 (D) 6.7 A Carnot heat engine operating between a warmer unknown temperature and a reservoir of boiling helium at 1.9 K has an efficiency of 13 %. What is the warmer temperature? 20. (A) 3.2 K (C) 1.4 K Change in internal energy is: (B) 0.2 K (D) 2.2 K (A) Q W (B) out in (C) / Q W Q m (D) 1 Q / Q cold hot 3

4 Isobaric work is: (A) Q W (B) P V (C) P T (D) V P A gas follows the PV trajectory shown in the figure. How much work is done per cycle by the gas if Po = 4.8 atm? (A) 840 J (B) 84 J (C) 192 J (D) 344 J Which of the following is a true statement? (A) It is impossible to convert work entirely into heat (B) It is impossible to transfer heat from a cooler body to a hotter body (C) The second law of thermodynamics is a consequence of the first law of thermodynamics (D) All of the statements are false An adiabatic process is performed on 9 moles of an ideal gas. The initial temperature is 315 K and the initial volume is 0.70 m 3. The final volume is 0.30 m 3. What is the amount of heat absorbed by the gas? (Use the adiabatic constant for the gas = 1.44) (A) 18 kj (B) 32 kj (C) 0 kj (D) 32 kj The second law of thermodynamics leads to the following conclusion: (A) the average temperature of the universe is increasing over time (B) it is theoretically possible to convert heat into work with 100% efficiency (C) disorder in the universe is increasing over time (D) total energy of the universe remains constant The statement that heat energy cannot be completely transformed into work is a statement of which thermodynamic law? (A) Third (C) First (B) Second (D) Fourth What is the change of entropy associated with 8 kg of water freezing to ice at 0 o C? (Use latent heat of fusion Lf = 80 kcal/kg) (A) 1.4 kcal/k (C) 2.3 kcal/k (B) 0 kcal/k (D) 1.4 kcal/k During an isothermal expansion, a confined ideal gas does 150 J of work against its surrounding. Which of the following describes the heat transfer during this process? (A) 150 J of heat was added to the gas (B) 150 J of heat was removed from the gas (C) 300 J of heat was added to the gas (D) 300 J of heat was removed from the gas 4

5 A confined ideal gas undergoes a cyclical process in three steps an isobaric step, followed by an isochoric step, followed by an isothermal step. Which of the following must be true? (A) The change in internal energy of the gas is equal to the work done during the isobaric step. (B) The change in internal energy of the gas is equal to the work done during the isobaric step minus the work done during the isothermal step (C) The total work done during the cycle is positive (D) The total work done during the cycle is equal but opposite to the net amount of heat Transferred If the temperature and volume of a sample of an ideal gas are both doubled, the pressure (A) decreases by a factor of 2 (B) increases by a factor of 2 (C) increases by a factor of 4 (D) remains unchanged 31. In three separate experiments, a gas is transformed from state along the paths (1, 2, and 3) illustrated in the figure below: The work done on the gas is (A) greatest for path 1 (B) least for path 2 (C) greatest for path 2 (D) the same for all three paths P i, V i to state P f, V f An ideal gas has is confined to a container whose volume is fixed. If the container holds n moles of gas, by what factor will the pressure increase if the absolute temperature is increased by a factor of 2? (A) 2 / ( nr ) (B) 2 (C) 2nR (D) 2/n What s the total work performed on the gas as it s transformed from state a to state c, along the path indicated? (A) 1,500 J (B) 3,000 J (C) 4,500 J (D) 9,500 J 34. A cylinder with a piston on top contains an ideal gas at an initial pressure P 1 volume V 1 and Temperature T 1. The gas is allowed to expand to twice its original volume in three different ways as shown. The mechanical work done by the gas is (A) greatest for path A (B) greatest for path B (C) greatest for path C (D) equal for all paths 5

6 35. A rigid, solid container of constant volume holds an ideal gas of volume V and temperature T, and pressure P. The temperature is increased in an isochoric process. Which of the following is NOT true? (A)The average speed of the molecules increases (B) The pressure increases (C) The kinetic energy of the system increases (D) The volume increases SHOW ALL WORK FOR THE FOLLOWING CALCULATIONS IN THE FORMAT REQUIRED 1. A sample of n moles of a monatomic ideal gas undergoes the cycle shown to the right. Processes A B, and C D are isovolumetric and process B C and D A are isobaric. At state A, the pressure is Po and the volume is Vo. Give all answers in terms of the given quantities and fundamental constants. (a) Determine the temperature at states A, B, C, and D. (b) Determine the heat transfer during process A B and state whether the heat is transferred into or out of the gas. (c) Determine the heat transfer during process B C and state whether the heat is transferred into or out of the gas. (d) Determine the net work performed during the cycle and state whether it is done on the gas or by the gas. (e) Determine the efficiency of this cycle and the maximum possible efficiency for a cycle operating between the highest and lowest temperatures in the cycle. 2. A gas undergoes a thermodynamic cycle, during which it absorbs 50 J of heat and exhausts 30 J of heat. What is the efficiency of the heat engine described by this cycle? 3. A Carnot engine using a monatomic ideal gas as a working substance operates between two reservoirs held at 300 K and 200 K, respectively. Starting at point A with pressure and volume as indicated on the graph, the gas expands isothermally to point B, where the volume is 4 x 10-3 m J of heat energy is absorbed by the gas in this process. (a) How many moles of gas are present? (b) Find the work done on the gas during the A B process. (c) Find the work done on the gas during the process B C, adiabatic expansion. (d) How much heat is expelled in the process C D? (e) Find the change in internal energy in the process D A. 6

7 4. An ideal gas is brought from A D by three different paths: ABD, AD, ACD. The temperature at A is the same as the temperature at D. Which of the following is true? (a) Process ABD occurs at constant temperature. (b) The work done by the gas along ABD is the same as the work done by the gas along ACD. (c) Net heat into the gas along ACD is greater than the work done by the gas along this path. (d) The change in the internal energy is the same for all three paths. (e) Work done by the gas along ACD is greater than the work done by the gas along AD J enters a Carnot engine from the hot reservoir, held at 400 K. During the entire cycle, 50 J of useful work is performed by the engine. What is the temperature of the cold reservoir? 6. During a certain process, 600 J of heat is added to a system. While this occurs, the system performs 200 J of work on the surroundings. The change in internal energy of the system is? 7. Which of the following is not true about thermal radiation? (a) It s a mechanism of energy exchange between systems at different temperatures. (b) It involves atomic excitations. (c) Ice at 0 0 C will emit thermal radiation. (d) It requires some material substance to travel through. (e) It s a byproduct of the food we eat mole of monatomic ideal gas is brought through a cycle A B C D A as depicted above. All processes are performed slowly. Respond to the following in terms of p0, V0, and R. (a) Find the temperature at each vertex. (b) Find the heat added to the gas for the process A B. (c) Find the work done on the gas for the process C D. (d) Find the heat added to the gas for the process D A. (e) Find the change in internal energy for (i) process B C (ii) the entire cycle 9. What s the maximum possible efficiency for a heat engine operating between heat reservoirs whose temperatures are C and C? 10. An engine receives 500 J from a heat reservoir at 800 K and rejects 320 J to the cold reservoir at 275 K find the actual efficiency and the theoretically maximal possible Carnot efficiency for this engine. 7

8 NAME: PERIOD: DATE: / / CHAPTER 15 WORKSHEET THERMODYNAMICS PHYSICSINMOTION CALCULATION PROBLEMS BOX IN ANSWERS Show all work use back if needed 8

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