A Carnot engine extracts heat from a block of mass m and specific heat c initially at temperature Th0 but without a heat source to maintain that temperature. The engine rejects heat to a reservoir at constant temperature Tc. The engine is operated so its mechanical power output is proportional to the temperature difference Th − Tc:
where Th is the instantaneous temperature of the hot block and P0, is the initial power. (a) Find an expression for Th as a function of time, and (b) determine how long it takes for the engine’s power output to reach zero.
Want to see the full answer?
Check out a sample textbook solutionChapter 19 Solutions
Essential University Physics: Volume 1 (3rd Edition)
Additional Science Textbook Solutions
Essential University Physics: Volume 2 (3rd Edition)
Introduction to Electrodynamics
Conceptual Integrated Science
College Physics (10th Edition)
Conceptual Physics (12th Edition)
Tutorials in Introductory Physics
- A multicylinder gasoline engine in an airplane, operating at 2.50 103 rev/min, takes in energy 7.89 103 J and exhausts 4.58 103 J for each revolution of the crankshaft. (a) How many liters of fuel does it consume in 1.00 h of operation if the heat of combustion of the fuel is equal to 4.03 107 J/L? (b) What is the mechanical power output of the engine? Ignore friction and express the answer in horsepower. (c) What is the torque exerted by the crankshaft on the load? (d) What power must the exhaust and cooling system transfer out of the engine?arrow_forwardIf a gas is compressed isothermally, which of the following statements is true? (a) Energy is transferred into the gas by heat. (b) No work is done on the gas. (c) The temperature of the gas increases. (d) The internal energy of the gas remains constant. (e) None of those statements is true.arrow_forwardA heat pump used for heating shown in Figure P18.25 is essentially an air conditioner installed backward. It extracts energy from colder air outside and deposits it in a warmer room. Suppose the ratio of the actual energy entering the room to the work done by the devices motor is 10.0% of the theoretical maximum ratio. Determine the energy entering the room per joule of work done by the motor given that the inside temperature is 20.0C and the outside temperature is 5.00C. Figure P18.25arrow_forward
- A heat pump has a coefficient of performance of 3.80 and operates with a power consumption of 7.03 103 W. (a) How much energy does it deliver into a home during 8.00 h of continuous operation? (b) How much energy does it extract from the outside air?arrow_forwardOne of a dilute diatomic gas occupying a volume of 10.00 L expands against a constant pressure of 2.000 atm when it is slowly heated. If the temperature of the gas rises by 10.00 K and 400.0 J of heat are added in the process, what is its final volume?arrow_forwardA thermodynamic system undergoes a process in which its internal energy decreases by 500 J. Over the same time interval, 220 J of work is done on the system. Find the energy transferred from it by heat.arrow_forward
- For a temperature increase of 10 at constant volume, what is the heat absorbed by (a) 3.0 mol of a dilute monatomic gas; (b) 0.50 mol of a dilute diatomic gas; and (c) 15 mol of a dilute polyatomic gas?arrow_forwardThe insulated cylinder shown below is closed at both ends and contains an insulating piston that is flee to move on frictionless bearings. The piston divides the chamber into two compartments containing gases A and B. Originally, each compartment has a volume of 5.0102 m3 and contains a monatomic ideal gas at a temperature of and a pressure of 1.0 atm. (a) How many moles of gas are in each compartment? (b) Heat Q is slowly added to A so that it expands and B is compressed until the pressure of both gases is 3.0 atm. Use the fact that the compression of B is adiabatic to determine the final volume of both gases. (c) What are their final temperatures? (d) What is the value of Q?arrow_forwardIn performing 100.0 J of work, an engine discharges 50.0 J of heat. What is the efficiency of the engine?arrow_forward
- When a gas undergoes an adiabatic expansion, which of the following statements is true? (a) The temperature of the gas does not change. (b) No work is done by the gas. (c) No energy is transferred to the gas by heat. (d) The internal energy of the gas does not change. (e) The pressure increases.arrow_forwardA heat engine operates between two temperatures such that the working substance of the engine absorbs 5000 J of heat from the high-temperature bath and discharges 3000 J to the low-temperature bath. The rest of the energy is converted into mechanical energy of the turbine. Find (a) the amount of work produced by the engine and (b) the efficiency of the engine.arrow_forwardConsider the process shown below. During steps AB and BC, 3600 J and 2400 J of heat, respectively, are added to the system. (a) Find the work done in each of the processes AB, BC, AD, and DC. (b) Find the internal energy change in processes AB and BC. (c) Find the internal energy difference between states C and A (d) Find the total heat added in the ADC process. (e) From the information given, can you find the heat added in process AD? Why or why not?arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Physics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning