Ch 2 - Written Problems - Sp24 2

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Apr 3, 2024

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Physics 132 Written Homework: Chapters 2 Problem 1: Isothermal and adiabatic processes A. In an adiabatic process no heat is allowed to flow to or from the gas. You compress 1 mole of gas adiabatically from 0.42m 3 to 0.12m 3 , starting at atmospheric pressure ( 1 × 10 5 Pa ). 1. Will the gas temperature increase, decrease or stay constant during the process? Explain. 2. Qualitatively sketch this process on the PV diagram at right. 3. Determine the work done on the gas. ( Hint : You’ll need the final pressure) 4. For this adiabatic compression, determine the signs of the following quantities: ࠵? = ࠵? = Δ࠵? = Δ࠵? = B. In an isothermal process the temperature of the gas is kept constant. You compress 1 mole of gas isothermally from 0.42m 3 to 0.12m 3 , starting at atmospheric pressure ( 1 × 10 5 Pa ). 1. At each volume value do you expect the pressure of the gas in this isothermal process to be bigger, smaller, or equal to the gas pressure in the previous adiabatic one? Explain. 2. Sketch this process on the PV diagram at right. Label appropriate values. 3. Shade the area on the graph that corresponds to the work done on the gas. 4. Determine the work done on the gas. 5. For this isothermal compression, determine the signs of the following quantities: Δ࠵? = Δ࠵? = ࠵? = ࠵? = P V P V Pv NRT Tx Vr const E 1 Part constant E 27T so temp is increasing We 11 0.3 2 1 1055 Wtioxtoff 2 0 0 It will be smaller be temp is constant which indicates that volume was decreased in order to maintain a constant temp Because of this change the pressure will also be decreased to maintain the balance 0.9 W mol 8.314 cons temp In 104 13 volume ratio is key Shah so 0 0 0
2 Problem 2: Thermodynamic cycle A thermodynamic cycle is a process that goes through some number of steps and then comes back to where it started. A 4-step cycle is shown in the picture at right, taking an ideal gas between states A , B , C , and D . At point A the pressure, volume and temperature of the gas are ࠵? ࠵? = 1.5 atm , ࠵? ࠵? = 0.4 m 3 , and ࠵? ࠵? = 120 K . The graph includes a grid of small squares, which can be helpful when calculating areas in the graph (related to the work on the gas) or getting information on the product of ࠵? and ࠵? (for instance, can you find 2 points in the graph where the gas has the same temperature?). It is also useful to learn about ratios of pressures or volumes at different states (for instance, the grid clearly shows that ࠵? ࠵? ࠵? ࠵? = 3 ). A. Describe the type of process for each step (i.e., isochoric heating, isobaric contraction, etc.) Explain how you can tell. If it is not one of the special processes, state so explicitly. 1. Step 1 ( A to B ): 2. Step 2 ( B to C ): 3. Step 3 ( C to D ): 4. Step 4 ( D to A ): B. Determine the temperature of the gas at each state ( Hint : the number of particles is unknown but constant: the ideal gas law could be useful to find equations for the ratios of temperatures). 1. State B : 2. State C : 3. State D : P V A B C D is EIIEj.it jaa nerdtted Images if 2m CP IEEE EE t i Iii ooo msn.so.az Isobaric compression w w W 105 0.5 1.5 5 105 Isochoric d Éu to du t w Q I If TA 6 87,2 6 120 d PBVB NRTB PcVC NRTC To 484 12041200J PDVD NRTD TD 1400T
3 C. How many particles ࠵? are in the gas? D. Next you will be applying the first law of thermodynamics to each step. 1. To determine the work done on the system during each process recall that in a PV -graph this corresponds to the area under the curve. Conveniently you could use the grid of squares to easily calculate these areas. How much work (in Joules) corresponds to a single square in the graph? 2. For each step use the graph to find ࠵? , the work done on the system. Do this by simply counting the number of squares under the graph and using your result for the work associated with each square (pay special attention to the signs!). For the curved path in step 2, approximate the area under the curve as best you can, by counting partial squares. 3. Using your knowledge of the temperature of the system at points A, B, C and D calculate the change in the internal energy of the system during each step. 60.94 6.022 102 3.67X10 parti.de 21013 105 0 5 n s 5 60 94m01 101325 015450662.5J AB 10 50662.5 5066255 Bsc 8.5 50662.5 430631.25 D A 50662.5 405300J A 0J B A 60.94 8.314 1200 200 1759982.24 2 60.94 8.314 400 1200 607986.1932 A D 60.94 8.314 200 400 1 151996 5552
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4 4. Finally, using the first law of thermodynamics determine ࠵? for each of the steps. Then complete the table below using your calculations. E. How much work is done on the system during one complete cycle? F. How much heat flows to the system during one complete cycle? (Hint: You can answer this without checking the heat flow during each step. Instead apply the first law of thermodynamics to the entire cycle. What is the change in internal energy of the system, after it’s come back to where it started?) Δ࠵? ࠵? ࠵? Step 1 ( A to B ): Step 2 ( B to C ): Step 3 ( C to D ): Step 4 ( D to A ): Q 506625 759982.74 1266607.745 430631.25 to 430631255 405300 607986.192 1013286.195 Of 1 151996.55 151996.555 759982.745 5066255 1266607.745 0 430631.255 430631.255 607986.1925 4053005 1013286.15J 1519961555 0 151996.555 506625 430631 25 405300 to tot 329306.25