An ideal gas with specific heat ratio γ 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?
(a)
Draw the
Answer to Problem 48P
The
Explanation of Solution
In this cycle, from
From
Figure 1 is the
Conclusion:
Therefore, the
(b)
The volume of the gas at the end of the adiabatic expansion.
Answer to Problem 48P
The volume of the gas at the end of the adiabatic expansion is
Explanation of Solution
Write the expression for the adiabatic process,
Here,
Conclusion:
Substitute
Rewrite the above equation for
Therefore, the volume of the gas at the end of the adiabatic expansion is
(c)
The temperature of the gas at the start of the expansion.
Answer to Problem 48P
The temperature of the gas at the start of the expansion is
Explanation of Solution
Write the expression for the ideal gas law,
Conclusion:
Substitute
Therefore, the temperature of the gas at the start of the expansion is
(d)
The temperature at the end of the cycle.
Answer to Problem 48P
The temperature at the end of the cycle is
Explanation of Solution
In this case, starting point is
Write the expression for the temperature at the end of the cycle,
Conclusion:
Therefore, the temperature at the end of the cycle is
(e)
The net work done on the gas during the cycle.
Answer to Problem 48P
The net work done on the gas during the cycle is
Explanation of Solution
Write the expression for the heat transferred during the cycle
Here,
Substitute
In an adiabatic process,
Here,
Write the expression for the ideal gas law,
Substitute
Write the expression for the heat transferred during the cycle
Here,
Substitute
Write the expression for the heat transferred for whole cycle,
Here,
Substitute (V), (VI) and (XII) in (XIII),
Write the expression for the internal energy change in the whole cycle,
Write the expression for the net work done on the gas during the cycle,
Conclusion:
Substitute
Therefore, the net work done on the gas during the cycle is
Want to see more full solutions like this?
Chapter 17 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_forwardTwo moles of a monatomic ideal gas such as oxygen is compressed adiabatically and reversibly from a state (3 atm, 5 L) to a state with a pressure of 4 atm. (a) Find the volume and temperature of the final state. (b) Find the temperature of the initial state. (c) Find work done by the gas in the process. (d) Find the change in internal energy in the process. Assume Cv=5R and Cp=Cv+R for the diatomic ideal gas in the conditions given.arrow_forwardA copper rod of cross-sectional area 5.0 cm2 and length 5.0 m conducts heat from a heat reservoir at 373 K to one at 273 K. What is the time rate of change of the universe's entropy for this process?arrow_forward
- A Carnot engine employs 1.5 mol of nitrogen gas as a working substance, which is considered as an ideal diatomic gas with =7.5 at the working temperatures of the engine. The Carnot cycle goes in the cycle ABCDA with AB being an isothermal expansion. The volume at points A and C of the cycle are 5.0103 m3 and 0.15 L, respectively. The engine operates between two thermal baths of temperature 500 K 300 K. (a) Find the values of volume at B and D. (b) How much heat is absorbed by the gas in the AB isothermal expansion? (c) How much work is done by the gas in the AB isothermal expansion? (d) How much heat is given up by the gas in the CD isothermal expansion? (e) How much work is done by the gas in the CD isothermal compression? (f) How much work is done by the gas in the BC adiabatic expansion? (g) How much work is done by the gas in the DA adiabatic compression? (h) Find the value of efficiency of the engine based on the net and heat input. Compare this value to the efficiency of a Carnot engine based on the temperatures of the baths.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_forwardAs shown below, calculate the work done by the gas in the quasi-static processes represented by the paths (a) AB; (b) ADB; (c) ACB; and (d) ADCB. `arrow_forward
- A monatomic ideal gas undergoes a quasi-static adiabatic expansion in which its volume is doubled. How is the pressure of the gas changed?arrow_forwardOf the following, which is not a statement of the second law of thermodynamics? (a) No heat engine operating in a cycle can absorb energy from a reservoir and use it entirely to do work, (b) No real engine operating between two energy reservoirs can be more efficient than a Carnot engine operating between the same two reservoirs, (c) When a system undergoes a change in state, the change in the internal energy of the system is the sum of the energy transferred to the system by heat and the work done on the system, (d) The entropy of the Universe increases in all natural processes, (e) Energy will not spontaneously transfer by heat from a cold object to a hot object.arrow_forwardWhich of the following is true for the entropy change of a system that undergoes a reversible, adiabatic process? (a) S 0 (b) S = 0 (c) S 0arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author: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, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning