(a)
Pressure and volume at given points.
(a)
Answer to Problem 61P
Volume at A, B, C, D are
Pressure at B and D are
Explanation of Solution
Write the ideal gas equation and rearrange for
Here
From figure, AB is isothermal.
Therefore.
Here
BC is adiabatic.
Therefore,
Here
Rearrange (II) in terms of
Rearrange (IV) in terms of
Similarly,
CD is isothermal.
Here
AD is adiabatic.
Substitute for
Rearrange (VIII) in terms of
Rearrange (II) and (VI) in terms of
Conclusion:
Substitute
Substitute
Substitute
Substitute
Volume at A, B, C, D are
Pressure at B and D are
(b)
Net work done per cycle.
(b)
Answer to Problem 61P
Net work done is
Explanation of Solution
Write the first law of
Here
As the change in internal energy is zero, (XI) becomes,
Write the equation for work done
Here
Write the equation for efficiency
Here
Rewrite (XIIII) in terms of
Conclusion:
Substitute
Net work done is
Want to see more full solutions like this?
Chapter 18 Solutions
Bundle: Principles of Physics: A Calculus-Based Text, 5th + WebAssign Printed Access Card for Serway/Jewett's Principles of Physics: A Calculus-Based Text, 5th Edition, Multi-Term
- At point A in a Carnot cycle, 2.34 mol of a monatomic ideal gas has a pressure of 1 4000 kPa, a volume of 10.0 L, and a temperature of 720 K. The gas expands isothermally to point B and then expands adiabatically to point C, where its volume is 24.0 L. An isothermal compression brings it to point D, where its volume is 15.0 L. An adiabatic process returns the gas to point A. (a) Determine all the unknown pressures, volumes, and temperatures as you f ill in the following table: (b) Find the energy added by heat, the work done by the engine, and the change in internal energy for each of the steps A B, B C, C D, and D A (c) Calculate the efficiency Wnet/|Qk|. (d) Show that the efficiency is equal to 1 - TC/TA, the Carnot efficiency.arrow_forwardThe compression ratio of an Otto cycle as shown in Figure 21.12 is VA/VB = 8.00. At the beginning A of the compression process, 500 cm3 of gas is at 100 kPa and 20.0C. At the beginning of the adiabatic expansion, the temperature is TC = 750C. Model the working fluid as an ideal gas with = 1.40. (a) Fill in this table to follow the states of the gas: (b) Fill in this table to follow the processes: (c) Identify the energy input |Qh|, (d) the energy exhaust |Qc|, and (e) the net output work Weng. (f) Calculate the efficiency. (g) Find the number of crankshaft revolutions per minute required for a one-cylinder engine to have an output power of 1.00 kW = 1.34 hp. Note: The thermodynamic cycle involves four piston strokes.arrow_forwardA sample of a monatomic ideal gas is contained in a cylinder with a piston. Its state is represented by the dot in the PV diagram shown in Figure OQ18.9. Arrows A through E represent isobaric, isothermal, adiabatic, and isovolumetric processes that the sample can undergo. In each process except D, the volume changes by a factor of 2. All five processes are reversible. Rank the processes according to the change in entropy of the gas from the largest positive value to the largest-magnitude negative value. In your rankings, display any cases of equality. Figure OQ18.9arrow_forward
- An idealized diesel engine operates in a cycle known as the air-standard diesel cycle shown in Figure P18.48. Fuel is sprayed into the cylinder at the point of maximum compression, B. Combustion occurs during the expansion B C, which is modeled as an isobaric process. Show that the efficiency of an engine operating in this idealized diesel cycle is e=11(TDTATCTB) Figure P18.48.arrow_forwardA 1.00-mol sample of an ideal monatomic gas is taken through the cycle shown in Figure P18.63. The process AB is a reversible isothermal expansion. Calculate (a) the net work done by the gas, (b) the energy added to the gas by heat, (c) the energy exhausted from the gas by heat, and (d) the efficiency of the cycle. (e) Explain how the efficiency compares with that of a Carnot engine operating between the same temperature extremes. Figure P18.63arrow_forwardAn ideal gas with specific heat ratio confined to a cylinder is put through a closed cycle. Initially, the gas is at Pi, Vi, and Ti. First, its pressure is tripled under constant volume. It then expands adiabatically to its original pressure and finally is compressed isobarically to its original volume. (a) Draw a PV diagram of this cycle. (b) Determine the volume at the end of the adiabatic expansion. Find (c) the temperature of the gas at the start of the adiabatic expansion and (d) the temperature at the end of the cycle. (e) What was the net work done on the gas for this cycle?arrow_forward
- One mole of an ideal gas is contained in a cylinder with a movable piston. The initial pressure, volume, and temperature are Pi , Vi , and Ti , respectively. Find the work done on the gas in the following processes. In operational terms, describe how to carry out each process and show each process on a PV diagram. (a) an isobaric compression in which the final volume is one-half the initial volume (b) an isothermal compression in which the final pressure is four times the initial pressure (c) an isovolumetric process in which the final pressure is three times the initial pressurearrow_forwardA heat engine using a monatomic gas follows the cycle shown in the ?? diagram. The gas starts out at point 1 with a volume of ?1=233 cm3, a pressure of ?1=235 kPa, and a temperature of 287 K. The gas is held at a constant volume while it is heated until its temperature reaches 455 K (point 2). The gas is then allowed to expand adiabatically until its pressure is again 235 kPa (point 3). The gas is maintained at this pressure while it is cooled back to its original temperature of 287K (point 1 again). For the first stage of this process, calculate in joules the heat ?12 transferred to the gas and the work ?12 done by the gas. ?12= ?12= For the second stage, calculate the heat ?23 transferred to the gas and the work ?23 done by the gas. ?23= ?23= For the third stage, calculate the heat ?31 transferred to the gas and the work ?31 done by the gas.arrow_forward2 moles of a monatomic ideal gas undergoes a cyclic process as depicted in the figure below. The processes AB and CD are isobaric and the process DA is adiabatic. For the given values PA= 11.5 atm, VA= 5.7 L, V3= 2.85 L, Pc=34.5 atm, and Vc=1.476 L answer the following questions. (use R=8.314 J 1 atm = 1.013x105 Pa, 1 L = 10-3 m³) . mol · K' Volume 1. Calculate the temperature TA= K 2. What type of process is the process BC? 3. Calculate the work done by the gas in the process DA. WDA = 4. Calculate the magnitude of the net heat entering the cycle. Q = 5. Calculate the magnitude of the net heat leaving the cycle. Qc = 6. Calculate the net work done by the gas. W= 7. Calculate the thermal efficiency of the cycle. e = % 8. Calculate the change in the entropy in the process AB. Include the sign (positive or negative) in your answer as well. ASAB = Karrow_forward
- A gas increases in pressure from 2.00 atm to 6.00 atm at a constant volume of 1.00 m3 and then expands at constant pressure to a volume of 3.00 m3 before returning to its initial state as shown in the figure below. How much work is done in one cycle? kJ A triangular path is plotted on a P V diagram that has a horizontal axis labeled V (m3), and a vertical axis labeled P (atm). The path is clockwise and runs through corner points in the following order: (1.00, 2.00), (1.00, 6.00), (3.00, 6.00).arrow_forwardanswer b and c pleasearrow_forwardA closed thermodynamic cycle described by an ellipse is shown on the PV diagram on the right. The maximum pressure of the system is 8.0 x 105 Pa, and the minimum pressure of the system is 4.0 x 10^5 Pa. The maximum volume of the system is 4.0 x 10^-3 m^3 and the minimum volume of the system is 2.0 x 10^-3 m^3 . a) Calculate the magnitude of the total work done by the system in one full cycle. b) Does this thermodynamic cycle describe what happens in an ENGINE or a REFRIDGERATOR/HEAT-PUMP?arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Physics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning