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.
(a)
The unknown pressures, volumes and the temperature in the table.
Answer to Problem 22.32P
The values of unknown pressures, volumes and the temperature in the table are,
|
|
| |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Explanation of Solution
Given: The number of moles of a mono atomic ideal gas is
Write the equation of adiabatic process
Here,
The value of
Substitute
Thus, the pressure of the gas at point
Write the ideal gas equation.
Here,
The value of gas constant is
Substitute
Thus, the temperature of the gas at point
In isothermal process, the temperature is constant.
For isothermal process
The temperature of the gas at point
Thus, the temperature of the gas at point
Write the ideal gas equation.
Here,
Substitute
Thus, the pressure of the gas at point
Write the equation of adiabatic process
Here,
Substitute
Thus, the volume of the gas at point
In isothermal process, the temperature is constant.
For isothermal process
The temperature of the gas at point
Thus, the temperature of the gas at point
Write the ideal gas equation.
Here,
Substitute
Thus, the pressure of the gas at point
Form a table and show the unknown value of pressures, volumes and temperatures.
|
|
| |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Conclusion:
Therefore, the values of unknown pressures, volumes and the temperature in the table are,
|
|
| |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
(b)
The energy added by heat, work done by the engine and the change in internal energy for each of the steps
Answer to Problem 22.32P
The values of energy added by heat, work done by the engine and the change in internal energy for each of the steps in the table are,
|
|
| |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Explanation of Solution
Given: The number of moles of a mono atomic ideal gas is
The process
Write the equation of change in temperature for process
Here,
Substitute
Thus, the change in internal energy for process
Write the equation of work done by the engine for process
Substitute
Thus, the work done by the engine for process
Write the equation of isothermal process
Substitute
Thus, the energy added by heat for process
Write the equation of change in temperature for process
Here,
The value of
Substitute
Substitute
Thus, the change in internal energy for process
The process
Thus, the energy added by heat for process
Write the equation of change in internal energy for process
Substitute
Thus, the work done by the engine for process
The process
Write the equation of change in temperature for process
Substitute
Thus, the change in internal energy for process
Write the equation of work done by the engine for process
Substitute
Thus, the work done by the engine for process
Write the equation of isothermal process
Substitute
Thus, the energy added by heat for process
Write the equation of change in temperature for process
Substitute
Substitute
Thus, the change in internal energy for process
The process
Thus, the energy added by heat for process
Write the equation of change in internal energy for process
Substitute
Thus, the work done by the engine for process
Form a table and show the value of energy added by heat, work done by the engine and the change in internal energy.
|
|
| |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Conclusion:
Therefore, the values of energy added by heat, work done by the engine and the change in internal energy for each of the steps in the table are,
|
|
| |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
(c)
The value of efficiency
Answer to Problem 22.32P
The value of efficiency
Explanation of Solution
Given: The number of moles of a mono atomic ideal gas is
Calculate the net work done from the table is,
Write the equation for efficiency.
Here,
Substitute
The value of efficiency
Conclusion:
Therefore, the value of efficiency
(d)
To show: The efficiency is equal to the Carnot efficiency
Answer to Problem 22.32P
The efficiency is equal to the Carnot efficiency
Explanation of Solution
Given: The number of moles of a mono atomic ideal gas is
Write the equation for Carnot efficiency.
Here,
The value of
Substitute
Thus, the Carnot efficiency is
Write the equation for efficiency.
Substitute
The value of efficiency is
Conclusion:
Therefore, the efficiency is equal to the Carnot efficiency
Want to see more full solutions like this?
Chapter 22 Solutions
Bundle: Physics for Scientists and Engineers, Technology Update, 9th Loose-leaf Version + WebAssign Printed Access Card, Multi-Term
- 13.87 ... Interplanetary Navigation. The most efficient way to send a spacecraft from the earth to another planet is by using a Hohmann transfer orbit (Fig. P13.87). If the orbits of the departure and destination planets are circular, the Hohmann transfer orbit is an elliptical orbit whose perihelion and aphelion are tangent to the orbits of the two planets. The rockets are fired briefly at the depar- ture planet to put the spacecraft into the transfer orbit; the spacecraft then coasts until it reaches the destination planet. The rockets are then fired again to put the spacecraft into the same orbit about the sun as the destination planet. (a) For a flight from earth to Mars, in what direction must the rockets be fired at the earth and at Mars: in the direction of motion, or opposite the direction of motion? What about for a flight from Mars to the earth? (b) How long does a one- way trip from the the earth to Mars take, between the firings of the rockets? (c) To reach Mars from the…arrow_forwardNo chatgpt pls will upvotearrow_forwarda cubic foot of argon at 20 degrees celsius is isentropically compressed from 1 atm to 425 KPa. What is the new temperature and density?arrow_forward
- Calculate the variance of the calculated accelerations. The free fall height was 1753 mm. The measured release and catch times were: 222.22 800.00 61.11 641.67 0.00 588.89 11.11 588.89 8.33 588.89 11.11 588.89 5.56 586.11 2.78 583.33 Give in the answer window the calculated repeated experiment variance in m/s2.arrow_forwardNo chatgpt pls will upvotearrow_forwardCan you help me solve the questions pleasearrow_forward
- Can you help me solve these questions please so i can see how to do itarrow_forwardHow can i solve this if n1 (refractive index of gas) and n2 (refractive index of plastic) is not known. And the brewsters angle isn't knownarrow_forward2. Consider the situation described in problem 1 where light emerges horizontally from ground level. Take k = 0.0020 m' and no = 1.0001 and find at which horizontal distance, x, the ray reaches a height of y = 1.5 m.arrow_forward
- 2-3. Consider the situation of the reflection of a pulse at the interface of two string described in the previous problem. In addition to the net disturbances being equal at the junction, the slope of the net disturbances must also be equal at the junction at all times. Given that p1 = 4.0 g/m, H2 = 9.0 g/m and Aj = 0.50 cm find 2. A, (Answer: -0.10 cm) and 3. Ay. (Answer: 0.40 cm)please I need to show all work step by step problems 2 and 3arrow_forwardFrom number 2 and 3 I just want to show all problems step by step please do not short cut look for formulaarrow_forwardPlz don't use chatgpt pls will upvotearrow_forward
- Physics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPrinciples 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 Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPhysics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning