Consider the relationship δeth=q+w. in this relationship, what does a positive value of w represent?

Mastering<strong>Physics</strong> <strong>Physics</strong> <strong>5D</strong> <strong>Fall</strong> <strong>2008</strong> Assignment 5 Due at 2:00pm on Tuesday, November 18, <strong>2008</strong> View Grading Details http://session.masteringphysics.com/myct Assignment Display Mode: View Printable Answers Isobaric, Isochoric, Isothermal, and Adiabatic Processes Description: Isobaric, isochoric, isothermal, and adiabatic processes on an ideal gas are examined using pV diagrams. Questions are posed about heat, work, and how they explain internal energy change using the first law of thermodynamics. Learning Goal: To recognize various types of processes on diagrams and to understand the relationship between - diagram geometry and the quantities , , and . The first law of thermodynamics is an expression of conservation of energy. This law states that changes in the internal energy of a system can be explained in terms of energy transfer into or out of the system in the form of heat and/or work . In this problem, we will write the first law of thermodynamics as Here "in" means that energy is being transferred into the system, thereby raising its internal energy, and "out" means that energy is leaving the system, thereby reducing its internal energy. You will determine the sizes of these energy transfers and classify their effect on the system as energy in or energy out. Consider a system consisting of an ideal gas confined within a container, one wall of which is a movable piston. Energy can be added to the gas in the form of heat by applying a flame to the outside of the container. Conversely, energy can also be removed from the gas in the form of heat by immersing the container in ice water. Energy can be added to the system in the form of work by pushing the piston in, thereby compressing the gas. Conversely, if the gas pushes the piston out, thereby pushing some atmosphere aside, the internal energy of the gas is reduced by the amount of work done. The internal energy of an ideal gas is directly proportional to its absolute temperature . An ideal gas also obeys the ideal gas law so the absolute temperature is directly proportional to the product of the absolute pressure and the volume . Here denotes the amount of gas in moles, which is a constant because the gas is confined, and is the universal gas constant. A diagram is a convenient way to track the pressure and volume of a system. Energy transfers by heat and/or work are associated with processes, which are lines or curves on the diagram taking the system from one state (i.e., one point on the diagram) to another. Work corresponds geometrically to the area under the curve on a diagram. If the volume increases (i.e., the system expands) the work will be classified as an energy output from the system. Part A What is the sign of as the system of ideal gas goes from point A to point B on the graph? Recall that is proportional to . Hint A.1 How to approach the problem Use the ideal gas law to figure out how the absolute temperature of the gas in state A compares to its absolute temperature in state B. Since the internal energy of an ideal gas is proportional to its absolute temperature, this will tell you how changes from state A to state B. ANSWER: The internal energy of the system increases, so is positive. The internal energy of the system decreases, so is negative. The states A and B have the same internal energy, so is zero. , cannot be determined without knowing the process used (i.e., the path taken) to get from state A to . 11/19/08 6:13 PM Page 1 of 27

11/17/2018 OA13: First Law of Thermodynamics and Heat engine OA13: First Law of Thermodynamics and Heat engine Due: 11:59pm on Wednesday, November 21, 2018 You will receive no credit for items you complete after the assignment is due. Grading Policy Conceptual Question 19.05 Part A In the first law of thermodynamics, Q is the heat gained by the system, that is, Q is positive if the system gains heat. ANSWER: True False Correct Conceptual Question 19.06 Part A In the first law of thermodynamics, W is the work done on the system, that is, W is positive if work is done on the system. ANSWER: True False Correct Conceptual Question 19.21 Part A FIGURE 19-2 https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=6545096 1/19 11/17/2018 OA13: First Law of Thermodynamics and Heat engine The process shown on the PV diagram in Fig. 19-2 is an ANSWER: adiabatic expansion. isovolumetric compression. isobaric expansion. isometric expansion. isothermal expansion. Correct Conceptual Question 19.22 Part A FIGURE 19-3 The process shown on the PV diagram in Fig. 19-3 is ANSWER: isothermal. adiabatic. idealistic. isochoric. isobaric. Correct https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=6545096 2/19 11/17/2018 OA13: First Law of Thermodynamics and Heat engine Conceptual Question 19.23 Part A In an isothermal process, there is no change in ANSWER: pressure. internal energy. temperature. volume. heat. Correct Conceptual Question 19.24 Part A A gas is quickly compressed in an isolated environment. During the event, the gas exchanged no heat with its surroundings. This process is ANSWER: idealistic. adiabatic. isobaric. isochoric. isothermal. Correct Conceptual Question 19.28 Part A When the first law of thermodynamics, Q = ΔU + W, is applied to an ideal gas that is taken through an adiabatic process, https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=6545096 3/19 11/17/2018 OA13: First Law of Thermodynamics and Heat engine ANSWER: W = 0. ΔU = 0. Q = 0. all of the above none of the above Correct Conceptual Question 19.27 Part A When the first law of thermodynamics, Q = ΔU + W, is applied to an ideal gas that is taken through an isothermal process, ANSWER: ΔU = 0 W=0 Q=0 all of the above none of the above Correct Expansion and Compression of a Gas Part A An ideal gas expands through an adiabatic process. Which of the following statements is/are true? Check all that apply. Hint 1. How to approach the problem To determine the correct statement(s) you need to apply the first law of thermodynamics. Note that when a gas expands it does work on its surroundings. Hint 2. First law of thermodynamics https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=6545096 4/19 11/17/2018 OA13: First Law of Thermodynamics and Heat engine When heat Q is added to a system, some of this added energy goes to increase the internal energy of the system by an amount ΔU . The remaining energy leaves the system as the system does work W on its surroundings. Thus, we have . Since W and Q may be positive, negative, or zero, we can also expect ΔU to be positive, negative or zero, depending on the process. ΔU = Q − W Hint 3. Adiabatic process An adiabatic process is a thermodynamic process in which no heat exchange occurs. ANSWER: The work done by the gas is negative, and heat must be added to the system. The work done by the gas is positive, and no heat exchange occurs. The internal energy of the system has increased. The internal energy of the system has decreased. Correct Part B After the adiabatic expansion described in the previous part, the system undergoes a compression that brings it back to its original state. Which of the following statements is/are true? Check all that apply. Hint 1. Internal energy in cyclic processes A process, or a sequence of processes, that brings the system back to its original state is called a cyclic process. In a cyclic process the total internal energy change is zero. ANSWER: The total change in internal energy of the system after the entire process of expansion and compression must be zero. The total change in internal energy of the system after the entire process of expansion and compression must be negative. The total change in temperature of the system after the entire process of expansion and compression must be positive. The total work done by the system must equal the amount of heat exchanged during the entire process of expansion and compression. Correct https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=6545096 5/19 11/17/2018 OA13: First Law of Thermodynamics and Heat engine Isobaric, Isochoric, Isothermal, and Adiabatic Processes Learning Goal: To recognize various types of processes on pV diagrams and to understand the relationship between pV -diagram geometry and the quantities Q, W , and ΔEth . The first law of thermodynamics is an expression of conservation of energy. This law states that changes in the internal energy of a system ΔEth can be explained in terms of energy transfer into or out of the system in the form of heat Q and/or work W . ΔEth = Q − W In this problem, we will write the first law of thermodynamics as ΔEth = Qin + Qout − Won − Wby . Here "in" means that energy is being transferred into the system by atomic-level collisions, thereby raising its internal energy ( Q > 0), and "out" means that energy is leaving the system, thereby reducing its internal energy (Q < 0). "On" means that energy is being transferred into the system by forces in a mechanical interaction, thereby raising the internal energy (W < 0), and "by" means that energy is leaving the system, thereby reducing the internal energy (W > 0). You will determine the sizes of these energy transfers and classify their effect on the system as energy in or energy out. Consider a system consisting of an ideal gas confined within a container, one wall of which is a movable piston. Energy can be added to the gas in the form of heat by applying a flame to the outside of the container. Conversely, energy can also be removed from the gas in the form of heat by immersing the container in ice water. Energy can be added to the system in the form of work by pushing the piston in, thereby compressing the gas. Conversely, if the gas pushes the piston out, thereby pushing some atmosphere aside, the internal energy of the gas is reduced by the amount of work done. The internal energy of an ideal gas is directly proportional to its absolute temperature T . An ideal gas also obeys the ideal gas law pV = nRT , so the absolute temperature T is directly proportional to the product of the absolute pressure p and the volume V . Here n denotes the amount of gas in moles, which is a constant because the gas is confined, and R is the universal gas constant. A pV diagram is a convenient way to track the pressure and volume of a system. Energy transfers by heat and/or work are associated with processes, which are lines or curves on the pV diagram taking the system from one state (i.e., one point on the diagram) to another. Work corresponds geometrically to the area under the curve on a pV diagram. If the volume increases (i.e., the system expands) the work will be classified as an energy output from the system. Part A What is the sign of ΔEth as the system of ideal gas goes from point A to point B on the graph? Recall that Eth is proportional to T . Hint 1. How to approach the problem Use the ideal gas law to figure out how the absolute temperature of the gas in state A compares to its absolute temperature in state B. Since the internal energy of an ideal gas is proportional to its absolute temperature, this will https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=6545096 6/19 11/17/2018 OA13: First Law of Thermodynamics and Heat engine tell you how Eth changes from state A to state B. ANSWER: The internal energy of the system increases, so ΔEth is positive. The internal energy of the system decreases, so ΔEth is negative. The states A and B have the same internal energy, so ΔEth is zero. ΔEth cannot be determined without knowing the process used (i.e., the path taken) to get from state A to state B Correct The value of Eth depends only on the state of the system. Thus ΔEth depends only on the endpoint states, not on the process followed that determines the path between the endpoint states. One possible way for the system to get from state A to state B is to follow a hyperbolic curve through point C, along which the product of pV is a constant. Temperature is proportional to the product pV , so this is a constant-temperature path, also known as an isothermal process. Part B How are Q and W related during this isothermal expansion? Hint 1. Find the sign of W is defined as the work done on the system, which in this case is the gas. Recall that the magnitude of the work done by the gas, Wgas, in going from one state of the gas to another is the area underneath the curve defined by the path. If the work done by the gas is nonzero, then the sign of Wgas is determined by the direction of the path. Since W = Wgas , which of the following describes W in Part B? W ANSWER: W < 0 W = 0 W > 0 https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=6545096 7/19 11/17/2018 OA13: First Law of Thermodynamics and Heat engine ANSWER: Both W and Q equal zero. Both W and Q provide energy input. Both W and Q provide energy output. W provides energy output, while Q provides energy input. They are equal in magnitude. W provides energy input, while Q provides energy output. They are equal in magnitude. Correct You can tell that the system is losing internal energy due to work because its volume is increasing. The internal energy change during any isothermal process involving an ideal gas is zero, so here the system must gain as much energy in the form of heat as it loses by doing work during this process. Another way to get from state A to state B is to go vertically from A to point D, holding volume constant, and then go horizontally to point B, holding pressure constant. A constant-volume path is called an isochoric process. A constant-pressure path is called an isobaric process. Part C How are Q and W related during the isochoric part of the overall path from state A to state D? Hint 1. How to approach the problem Use the ideal gas law to determine how the absolute temperature of the gas in state A compares to its absolute temperature in state D. This will help you determine whether the net energy transfer is in or out, since the internal energy of an ideal gas is proportional to its absolute temperature. ANSWER: https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=6545096 8/19 11/17/2018 OA13: First Law of Thermodynamics and Heat engine Both Q and W equal zero. Q provides energy input, while W equals zero. Q provides energy output, while W equals zero. Q provides energy input, while W provides energy output. Q provides energy output, while W provides energy input. Correct You can tell that the system is losing internal energy since its temperature goes down (since pV goes down). No work is done during any isochoric process, since no area accumulates under a vertical curve. Hence energy transfer in the form of heat must account for the entire internal energy change. Part D How are Q and W related during the isobaric part of the overall path from state D to state B? ANSWER: Both W and Q provide energy input. Both W and Q provide energy output. W provides energy output, while Q provides energy input. They are equal in magnitude. W provides energy output, while Q provides energy input; W is larger. W provides energy output, while Q provides energy input; Q is larger. Correct In going from state A to state D the system loses internal energy. Since the overall change of internal energy from state A to state B is zero, during the isobaric part of the overall process the system internal energy must increase. Since the system is expanding, internal energy is lost from the system due to work. Hence Q must exceed W (in magnitude) to explain the net increase in internal energy. Another way to get from state A to state B is to follow an adiabatic path from state A to state E, in which no heat energy transfer is allowed, and then to follow an isochoric path from state E vertically to state B. Notice that during the adiabatic part of this path, from state A to state E, Q = 0 by definition and internal energy is lost due to work since the system is expanding. https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=6545096 9/19 11/17/2018 OA13: First Law of Thermodynamics and Heat engine Part E Which of the following statements are true about the isochoric part of the overall path, from state E to state B? Check all that apply. Hint 1. How to approach the problem Recall that the total internal energy change from state A to state B is zero. This means that the isochoric process must undo any changes to internal energy made during the adiabatic process. ANSWER: W is zero. Q provides energy input. T decreases. Eth increases. Correct Since no work is allowed in isochoric processes, Q must serve as an energy input to explain the increase in both absolute temperature and internal energy. One more way to get from state A to state B is to follow a direct path through state F. This process is not isobaric, isochoric, isothermal, or adiabatic, yet you can draw some conclusions about its energetics using the first law of thermodynamics. https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=6545096 10/19 11/17/2018 OA13: First Law of Thermodynamics and Heat engine Part F Which of the following statements are true about the first half of this process, just going from state A to state F? Check all that apply. ANSWER: Both T and Eth increase. W provides energy input. Q provides energy input. Q is larger (in magnitude) than W . Correct State F has a larger pV value than state A, so the internal energy increases in this part of the process. Since the system is expanding, internal energy is lost from the system due to work. Hence Q must exceed W (in magnitude) to explain the net increase in internal energy. Understanding what happens during the second half of the process, going from state F to state B, is more subtle. The temperature and the internal energy both go down. Since the system continues to expand, W provides energy output. However, it is challenging to determine whether Q provides energy input or energy output from state F to state B. Can you figure it out? Problem 19.31 Part A A certain amount of a monatomic gas is maintained at constant volume as it is cooled by 50 K. This feat is accomplished by removing 400 J of energy from the gas. How much work is done by the gas? ANSWER: https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=6545096 11/19 11/17/2018 OA13: First Law of Thermodynamics and Heat engine zero 200 J 400 J -400 J none of the above Correct Problem 19.24 Part A During an isothermal process, 5.0 J of heat is removed from an ideal gas. What is the change in internal energy? ANSWER: zero 7.5 J 2.5 J 5.0 J 10 J Correct Problem 19.27 Part A 200 J of work is done in compressing a gas adiabatically. What is the change in internal energy of the gas? ANSWER: https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=6545096 12/19 11/17/2018 OA13: First Law of Thermodynamics and Heat engine 200 J 150 J zero 100 J There is not enough information to determine. Correct Problem 19.34 In an engine, an almost ideal gas is compressed adiabatically to half its volume. In doing so, 2810 J of work is done on the gas. Part A How much heat flows into or out of the gas? ANSWER: Q = 0 J Correct Part B What is the change in internal energy of the gas? ANSWER: ΔEint = 2810 J Correct Part C Does its temperature rise or fall? ANSWER: fall rise Correct https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=6545096 13/19 11/17/2018 OA13: First Law of Thermodynamics and Heat engine Problem 19.53 A 3.20 mol sample of an ideal diatomic gas expands adiabatically from a volume of 0.1780 m3 to 0.783 m3 . Initially the pressure was 1.00 atm. Part A Determine the initial and final temperatures. Enter your answers numerically separated by a comma. ANSWER: , Ti Tf = 678,375 K Correct Part B Determine the change in internal energy. ANSWER: ΔEint = −2.02×104 J Correct Part C Determine the heat lost by the gas. ANSWER: Q = 0 J Correct Part D Determine the work done on the gas. (Assume no molecular vibration.) ANSWER: W on gas = −2.02×104 J Correct https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=6545096 14/19 11/17/2018 OA13: First Law of Thermodynamics and Heat engine Simple Ways of Expanding A plot of pressure as a function of volume is known as a pV diagram. pV diagrams are often used in analyzing thermodynamic processes. Consider an ideal gas that starts in state O, as indicated in the diagram. Your task is to describe how the gas proceeds to one of four different states, along the different curves indicated. Although there are an infinite number of such curves, several are particularly simple because one quantity or another does not change: Adiabatic: ΔQ = 0 . No heat is added or subtracted. Isothermal: ΔT = 0. The temperature does not change. (The prefix "iso" means equal or alike.) Isobaric: Δp = 0. The pressure does not change. (A barometer measures the pressure.) Isochoric: ΔV = 0. The volume does not change. (This process is infrequently used.) The key idea in determining which of these processes is occurring from a pV plot is to recall that an ideal gas must obey the ideal gas equation of state: pV = N kB T (where the constant kB is the Boltzmann constant, which has the value 1.381 × 10 −23 J/K in SI units). Generally N , the number of gas particles, is held constant, so you can determine what happens to T at various points along the curve on the pV diagram. Note that in this problem, as is usually assumed, the processes happen slowly enough that the gas remains in equilibrium without hot spots, without propagating pressure waves from a rapid change in volume, or without involving similar nonequilibrium phenomena. Indeed, the word "adiabatic" is often used by scientists to describe a process that happens slowly and smoothly without irreversible changes in the system. Part A What type of process does curve OA represent? Hint 1. What quanitity remains constant? Curve OA is horizontal; the pressure of the system remains constant throughout this process. What is the name of a process in which pressure remains constant? ANSWER: adiabatic isobaric isochoric isothermal Correct Part B https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=6545096 15/19 11/17/2018 OA13: First Law of Thermodynamics and Heat engine What type of process does curve OC represent? Hint 1. Relationship between pressure and volume When V /V0 = 2, p/p0 = 1/2; when V /V0 = 4 , p/p0 = 1/4 . Evidently, pressure is proportional to the inverse of the volume. What is the name of a process in which p is proportional to 1/V ? Hint 2. Use the ideal gas law Recall the ideal gas equation of state for a fixed amount of gas: pV = cT , where c is some constant. Solving this equation for p yields p = cT /V . If p is to be proportional to 1/V , the temperature T must remain constant throughout the process. What is the name of a process in which temperature remains constant? ANSWER: adiabatic isobaric isochoric isothermal Correct Detailed analysis of curve OB The following questions refer to the process represented by curve OB, in which an ideal gas proceeds from state O to state B. Part C The pressure of the system in state B is __________ the pressure of the system in state O. ANSWER: greater than less than equal to Correct Part D The work done by the system is __________. Hint 1. How to find the work done using the pV diagram On a pV diagram, the work done during a particular process is represented by the area under the curve describing that process. Is the area under curve OB greater than, less than, or equal to zero? https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=6545096 16/19 11/17/2018 OA13: First Law of Thermodynamics and Heat engine ANSWER: greater than zero less than zero equal to zero Correct Part E The temperature of the system in state B is __________ the temperature of the system in state O. Hint 1. Compare curve OB to an isothermal process Does curve OB lie above or below a curve representing an isothermal (constant-temperature) process? Use this, along with the ideal gas equation of state, to figure out how T changes as the system proceeds from state O to state B. Hint 2. Computing the change in temperature mathematically The ideal gas equation of state for a fixed amount of gas is pV = cT , where c is some constant. To find the sign of the change in temperature, you could find (p/p0 )(V /V0 ) at point B, then subtract the value of (p/p0 )(V /V0 ) at point O. Although this method will not yield the actual change in temperature, it will give a number proportional to the change in temperature (with the proper sign). ANSWER: greater than less than equal to Correct Part F The internal energy of the system in state B is __________ the internal energy of the system in state O. Hint 1. Relationship between internal energy and temperature The change in internal energy of an ideal gas is proportional to its change in temperature; the constant of proportionality is the heat capacity at constant volume. ANSWER: https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=6545096 17/19 11/17/2018 OA13: First Law of Thermodynamics and Heat engine greater than less than equal to Correct Problem 19.86 Suppose 3 mol of neon (an ideal monatomic gas) at STP are compressed slowly and isothermally to 0.19 the original volume. The gas is then allowed to expand quickly and adiabatically back to its original volume. Part A Find the highest temperature attained by the gas. Express your answer using three significant figures. ANSWER: Tmax = 273 K Correct Part B Find the lowest temperature attained by the gas. Express your answer using two significant figures. ANSWER: Tmin = 90 K Correct Part C Find the highest pressure attained by the gas. Express your answer using two significant figures. ANSWER: P max = 5.3 atm Correct https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=6545096 18/19 11/17/2018 OA13: First Law of Thermodynamics and Heat engine Part D Find the lowest pressure attained by the gas. Express your answer using two significant figures. ANSWER: P min = 0.33 atm Correct Score Summary: Your score on this assignment is 91.2%. You received 127.66 out of a possible total of 140 points. https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=6545096

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