What is Carnot: Definition and 292 Discussions

The Carnot cycle is a theoretical ideal thermodynamic cycle proposed by French physicist Nicolas Léonard Sadi Carnot in 1824 and expanded upon by others over the next few decades. It provides an upper limit on the efficiency that any classical thermodynamic engine can achieve during the conversion of heat into work, or conversely, the efficiency of a refrigeration system in creating a temperature difference by the application of work to the system. It is not an actual thermodynamic cycle but is a theoretical construct.
Every single thermodynamic system exists in a particular state. When a system is taken through a series of different states and finally returned to its initial state, a thermodynamic cycle is said to have occurred. In the process of going through this cycle, the system may perform work on its surroundings, for example by moving a piston, thereby acting as a heat engine. A system undergoing a Carnot cycle is called a Carnot heat engine, although such a "perfect" engine is only a theoretical construct and cannot be built in practice. However, a microscopic Carnot heat engine has been designed and run.Essentially, there are two "heat reservoirs" forming part of the heat engine at temperatures Th and Tc (hot and cold respectively). They have such large thermal capacity that their temperatures are practically unaffected by a single cycle. Since the cycle is theoretically reversible, there is no generation of entropy during the cycle; entropy is conserved. During the cycle, an arbitrary amount of entropy ΔS is extracted from the hot reservoir, and deposited in the cold reservoir. Since there is no volume change in either reservoir, they do no work, and during the cycle, an amount of energy ThΔS is extracted from the hot reservoir and a smaller amount of energy TcΔS is deposited in the cold reservoir. The difference in the two energies (Th−Tc)ΔS is equal to the work done by the engine.

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  1. T

    Comparing Carnot & Ranking Cycles + Steady Flow Energy Equation

    Please i need answer for this questions A- compare the Carnot cycle with the Ranking Cycle B- State The Steady Flow Energy equation and discuss the Origin and definition of each of the terms c- A vapour compression refrigeration using ammonia works at a condenser temperature of 40C and...
  2. S

    Thermodynamics Help- Proving Carnot Cycle

    1. Please help with the following question. Given: A Heat engine goes through a Carnot Cycle as the following states: State 2 to 3: air compresses adiabatically (pressure increasing) State 3 to 4: air expanded under isobaric process State 4 to 1: air goes under adiabatic expansion process...
  3. R

    What is tha graph of carnot cycle

    what is the graph of carnot cycle in P-V plane using black body radiation? given the internal energy U=aVT^4 where a is the stefan's constant and P=(1/3)aT^4. thank you
  4. M

    Entropy change in carnot cycle

    Is it true that for a Carnot cycle, the entropy change for the whole system (engine plus the two reservoirs) would add up to zero? I am reasoning that it would, by the Clausius theorem that for a reversible cycle (which a Carnot cycle is), the entropy change is zero. Otherwise it would not be...
  5. R

    Exploring Work Output of a Carnot Cycle

    Hi From http://en.wikipedia.org/wiki/Carnot_cycle "Reversible isothermal expansion of the gas at the "hot" temperature, TH (isothermal heat addition). During this step the expanding gas makes the piston work on the surroundings. The gas expansion is propelled by absorption of quantity Q1 of...
  6. Z

    Carnot engine ( Thermodynamics )

    Homework Statement 8. A house is cooled by an air conditioner. The outside temperature is 32°C and the inside temperature is 21°C. The heat leakage into the house is 9000 kcal/hr. If the air conditioner has the efficiency of a Carnot engine, what is the mechanical power required to keep the...
  7. S

    Why is the Carnot Cycle so Important?

    All reversible cyclic processes (engines) have the same efficiency: 1-T2/T1. And Carnot demostrated this efficiency with the Carnot Cycle and went on to use this to demonstrate that this was the upper limit for efficiency. My question is, why is it that there is such importance placed on...
  8. M

    Maximizing Efficiency in Tandem Carnot Engines

    Please help with the following: Prove that the efficiency of two carnot engines operating in tandem, one going from a cold reservoir of temperature Tc to a hot reservoir of Ti, then the second going from a cold reservoir of temperature Ti, to a hot reservoir of temperature Th must be less than...
  9. C

    Carnot engine, T-S diagram.

    Homework Statement I have to draw a temperature versus entropy for a carnot engine. My solutions say that as a parallel to the PV diagram, the adiabatics on the TS diagram are vertical, going from t2 to t1 and vise versa. My question is really how an adiabatic change results in a temperature...
  10. smokingwheels

    Does the Carnot heat engine law apply to an internal combustion engine?

    The law says that the maximum thermal efficiency of a heat engine can be 88%. If I have and internal combustion engine using 9.8 cc/min instead of 25 to 30 cc/min and the other accepted figure is a 2L 4 cylinder engine for idle is it uses approx 5 HP of fuel just just to idle. So I am doing...
  11. T

    Carnot Heat Engine, thermodynamics

    A carnot engine has an efficiency of 59% and performs 2.5x104 J of work in each cycle. a) how much heat does the engine extract from its heat source in each cycle? b) suppose the engine exhausts heat at room temp (20oC) what is the temperature of the heat source? I know that the...
  12. R

    What is the minimum work needed to cool an object using a carnot refrigerator?

    Homework Statement 433J of heat is extracted from a massive object at 0\circC while rejecting heat to a hot reservoir at 19\circC. What minimum amount of work will accomplish this? Answer in units of J. Homework Equations COP= Qc/(Qh-Qc) = Tc/(Th-Tc) The Attempt at a Solution...
  13. N

    Carnot cycles in thermodynamics

    Homework Statement A heat engine operates in a Carnot cycle between 75.0°C and 353°C. It absorbs 21000 J of energy per cycle from the hot reservoir. The duration of each cycle is 2.00 s. Homework Equations W=Qc-Qh, W=-P change in temperature The Attempt at a Solution I attempted to...
  14. F

    Carnot Heat Pumps: Solving |Q_c|/|Q_h|=T_c/T_h Equation

    A Carnot engine uses hot and cold reservoirs that have temperatures of 1684 and 842 K, respectively. The input heat for this engine is |QH|. The work delivered by the engine is used to operate a Carnot heat pump. The pump removes heat from the 842-K reservoir and puts it into a hot reservoir at...
  15. F

    Carnot Heat Pump: Solving |Q_c|/|Q_h|=T_c/T_h

    A Carnot engine uses hot and cold reservoirs that have temperatures of 1684 and 842 K, respectively. The input heat for this engine is |QH|. The work delivered by the engine is used to operate a Carnot heat pump. The pump removes heat from the 842-K reservoir and puts it into a hot reservoir...
  16. K

    Carnot Heat Engine to Carnot Heat Pump

    We have a carnot engine with Th = 800 degrees Celsius, and Tc = 50 degrees Celsius. This produces a work which is drives a carnot heat pump which has heat reservoirs at Th' = 50 degrees celsius and Tc' = 0 degress Celsius. What is the ratio of heat absorbed by the Heat Engine to the heat...
  17. M

    Carnot Cycle Question: Heat Transfer and Pressure Changes Explained

    Homework Statement Dear All, I have a question regarding the Carnot Cycle: (The image is taken from Wikipedia, I hope that is not a problem... In case it is I will change it.) Points one to two are an isothermal reaction. The gas, kept at constant temperature, is expanding, the...
  18. T

    Solving Entropy of Carnot Engine for Homework

    Homework Statement You want to boil a pot of water at 20C by heating it to 100C. I suggest a way of heating the pot in a reversible manner: simply inserting a Carnot engine between the reservoir (at 100C) and the pot. The Carnot engine operates between two temperatures, absorbing heat dQ_1...
  19. T

    What is the thermal efficiency of an ideal gas cycle?

    Homework Statement A possible ideal gas cycle operates as follows: (i) From an initial state (p_1,V_1), the gas is cooled at constant pressure to (p_1,V_2); (ii) the gas is heated at constant volume to (p_2,V_2); (iii) the gas expands adiabatically back to (p_1,V_1). Assuming...
  20. N

    AZING! Understanding the Carnot Cycle: Heat, Work, and Internal Energy

    Homework Statement I don't understand the process between the points in a carnot cycle. Homework Equations Can someone please explain what is going on from point to point in terms of Q (heat), U(thermal energy), and Work? The Attempt at a Solution
  21. S

    Ideal Gas Carnot engine refrigeration

    Homework Statement What is the relationship between the heat absorbed and rejected by the reservoirs and their temperature. If a heat pump is used to transfer heat what is the rate at which heat is added to the hot reservoir in terms of the temperatures of the reservoir and the work done by...
  22. N

    Thermodynamics - Carnot Engine

    Homework Statement (a.) For an Ideal Gas Carnot engine, what is the relationship between heat absorbed and rejected by the reservoirs and their temperature? If a heat pump is used to transfer this heat, what is the rate at which heat is added to the hot reservoir in terms of the temperatures of...
  23. R

    Carnot refrigerator cost problem

    Homework Statement Three kilograms of liquid water at 0° C is put into the freezer compartment of a Carnot refrigerator. The temperature of the compartment is -13.5° C, and the temperature of the kitchen is 24.5° C. If the cost of electrical energy is ten cents per kilowatt · hour, how much...
  24. M

    Thermodynamics: Carnot Engine, WHY IS Qhot NEGATIVE?

    Homework Statement 1. A heat engine operating between 200°C and 80.0°C achieves 20.0% of the maximum possible efficiency. What energy input will enable the engine to perform 10.0 kJ of work? Homework Equations e =1- Tc/Th W=e*Qh The Attempt at a Solution I got the answer but I...
  25. S

    Carnot Refrigerator at Phase Boundry

    Hi All, My textbook mentions that the coefficient of refrigeration for a Carnot refrigerator acting between a hot reservoir T_{H} and a cold reservoir T_{C} is K_{Carnot} = \frac{T_C}{T_H - T_C} This got me wondering - Suppose you had 1 kg of ice at it's melting point, and 1 kg of water...
  26. J

    Engine Cycles: Otto, Diesel and Carnot

    Problem / Question 1)Study the engine cycles for the Otto cycle, Diesel cycle, the Carnot cycle and the standard air cycle. Explain the principles of how they work why they are different and the benefits and disadvantages of each of the systems. I have wrote about the otto cycle...
  27. T

    Maximum Work from Carnot Engine

    Homework Statement A 200 litre container of boiling water and a 200 litre container of ice cold water are used as heat source and sink for a Carnot engine. Calculate the maximum amount of useful work that can be obtained from the system and the final temperature of the two containers of...
  28. K

    Which Temperature Adjustment Improves Carnot Engine Efficiency More?

    Homework Statement Determine which gives the higher efficiency of a Carnot engine, increasing the temperature of the hot reservoir, or decreasing the temperature of the cold reservoir by the same amount. Justify your answer carefully. Homework Equations (TH-TC)/TH)The Attempt at a Solution By...
  29. I

    Carnot refrigerator problem

    Homework Statement can you please help me solve this problem? A carnot refrigerator takes heat from water @ 0 degrees celsius and rejects heat to a room at 27 degrees celsius. If 50 kg of water @ 0 degrees celsius is converted to ice @ 0 degrees celsius, how much energy must be supplied...
  30. U

    Why Are Carnot Cycle Calculations So Confusing?

    Nevermind for now, just redid the whole thing and saw I made a stupid little mistake in computing the first volumes that messed everything else up. A Carnot engineer operating with a perfect gas between 800C and 25C has an operating pressure range between 20kPa and 6000kPa. Determine the work...
  31. M

    Reverse Carnot Engine (Heat Pump)

    Homework Statement A house is heated by means of a carnot engine operating in reverse (Heat Pump). The outside Temperature (Tc) is 270k, and the required inside temperature (Th) is 300k. If heating the house to this temperature normally requires 10kW of electrical heating, how much power is...
  32. S

    Thermodynamics/Statisical Mechanics: Carnot Cycle

    Homework Statement Consider a Carnot Cycle that absorbs heat from the hot reservoir at Thw and expels to the cold reservoir at Tcw just below Th and above Tc respectively. a.) Derive an equation that relates the four temperatures. b.) Using the first and second law, write down an...
  33. D

    Carnot Refrigerator Homework: Coeff of Performance, Work & Heat

    Homework Statement A Carnot refrigerator operating between -30.0 ^ C and + 20.0 ^ C extracts heat from the cold reservoir at the rate 300 J/s. What are (a) the coefficient of performance of this refrigerator, (b) the rate at which work is done on the refrigerator and (c) the rate at which heat...
  34. A

    Calculating temperatures of reservoirs in Carnot engine

    Homework Statement An ideal monatomic gas is the working substance of a Carnot engine. During the isothermal expansion, the volume doubles. The ratio of the final volume to the initial volume in the adiabatic expansion is 5.7. The work output of the engine is 9x10^{5}J in each cycle. Compute...
  35. Q

    Energy vs. entropy plot for a Carnot cycle

    Homework Statement I'm trying to understand how one would plot this. Homework Equations dS = dQ/T dU = dQ-dW (W is work done by the system, Q is heat absorbed by system, U is energy) For a closed cycle, dU = 0. Carnot Cycle: 1- isothermal expansion at Th 2- adiabatic expansion to Tc...
  36. K

    If i build a carnot engine in the real world, is its efficiney smaller than 1-t2/t1?

    I think it is due to friction and the carnot efficiency is derived in a reversible cycle. Also,can i build just a little bit irreversible but still carnot? But if irreversible how can i draw the graph? Still smooth line?
  37. J

    How Does Changing Temperatures Affect Carnot Engine Efficiency?

    Homework Statement A Carnot heat engine operates between temperatures Th and Tc. (a) If Th = 515 K and Tc = 363 K, what is the efficiency of the engine? 0.30 Your answer is correct. (b) What is the change in its efficiency for each degree of increase in Th above 515 K? ? K-1 (c) What...
  38. N

    Contradiction/breach 2nd law? Simply with carnot engine + negative temperature

    Hello, For a reversible heat engine between temperatures T_1 and T_2, the ratio of heat going in and out the engine is \frac{Q_1}{Q_2} = \frac{T_1}{T_2} (second law). Say T_1 = 200 K and T_2 = 273 K, then heat goes from 2 to 1 and as we can see, the ratio of heat that goes in the engine is...
  39. M

    Finding the Exhaust Temperature of a Carnot Engine

    Homework Statement A Carnot engine performs work at the rate of 360 kW while using 720 kcal of heat per second.If the temperature of the heat source is 650 C, at what temperature is the waste heat exhausted? Homework Equations because Th,Qh,and W are given so i going to use this formula...
  40. C

    Entropy chance with a carnot cycle?

    in a carnot cycle the gas expands adiabatically from 200 degrees to 500 degrees. what is the efficecy? and what is the entropy change of the gas during the expansion? sorry - i got the efficiency to be: 38.8% however I am unsure how to work out the entropy chance? any hints?
  41. P

    Carnot cycle with efficiency > 1

    Is it possible (at least theoretically) to construct engine which uses Carnot cycle and two reservoirs with temperatures T_1<0<T_2 (one of them has negative temperature which is possible e.g. in case of two-state paramagnet). Such cycle would have efficiency greater then 1. (of course the...
  42. C

    Need help with a question involving heat engines, the carnot cycle and entropy.

    The Attempt at a Solution For a) I imagine it is easier to control the temperature of the hot reservoir because you could use a constant heat source e.g. bunsen burner. c) melting/freezing water. d) Entropy of the environment increases and the entropy of the universe always increases...
  43. F

    A Carnot engine. Got right answers, but I have questions on solution.

    Homework Statement A Carnot engine runs between a high temperature of 500 C and a low temperature of 50 C. The isothermal expansion (upper branch) occurs between a volume of 0.5L and 1.0L. The isothermal contraction (lower branch) occurs between 2.0L and 1.0L. There are 2 moles of gas...
  44. M

    Carnot Air Conditioner Question.

    Q: A Carnot air conditioner operates between an indoor temp of 20C and an outdoor temp of 39C, how much ENERGY does it need to remove 2000 J of heat from the interior of the house? A: 130J i got 121J O.o?
  45. N

    Carnot engine air conditioner

    A Carnot air conditioner takes energy from the thermal energy of a room at 76°F and transfers it as heat to the outdoors, which is at 96°F. For each joule of electric energy required to operate the air conditioner, how many joules are removed from the room? Attempt at problem 76 + 273 = 349 96...
  46. V

    AT: Calculating Temperature T for Two Carnot Engines in Series

    Homework Statement Two heat engines operating on Carnot cycles are arranged in series. The first engine A receives heat at 927 deg C and rejects heat to a reservoir at a temperature T. The second engine B receives the heat rejected by the first engine, and in turn rejects heat to a reservoir...
  47. V

    Carnot refrigerator and energy

    Homework Statement a carnot refrigerator takes heat from water at 0 degree celsius and rejects heat to a room at 27 degree celsius. if 50kg of water at 0 degree celsius is converted to ice at 0 degree celsius. how much energy must be supplied to the refrigerator? Homework Equations Sorry, i...
  48. D

    Carnot efficiency: is heat always positive?

    This is a very quick question but in the equation e=1-Q_{C}/Q_{H} do we treat both Q's as positive even though heat goes in in one case and out in the other? Or is there some detail I'm missing that would otherwise make the result less than 1.
  49. C

    Solving Carnot Heat Engine: Tf = SQRT(TcTh)

    Homework Statement A heat pump takes heat from a hot resevoir and dissipates heat to a cold one. Both resevoirs are equal mass and specific heat capacity. Show that as the heat engine does maximal work the final temp of the resevoirs = Tf = SQRT(TcTh) Homework Equations Qin = Wout +...
  50. S

    Intake Temperature for a 40.2% Efficient Carnot Engine

    Homework Statement The exhaust temperature of a Carnot heat engine is 401◦ C. What is the intake temperature if the efficiency of the engine is 40.2 %? Answer in units of ◦ C. Homework Equations e = 1 - Tc/Th (all in Kelvin) The Attempt at a Solution 0.402 = 1 - Tc/ (401+273) = 1...
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