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. J

    Is a Sun-Solar Cell System Truly Equivalent to a Carnot Engine?

    I have undertaken a course on Semiconductors. My professor told us that a sun-solar cell system can be taken as a Carnot Engine. He assumed that the surface temperature of sun is 6000k and that of solar cell is 300k.And then he found out the efficiency by (1-T1/T2), which came out close to be...
  2. junfan02

    Carnot Engine: Finding Final Temperature Attained

    A Carnot engine is operating between a source and a sink at temperatures T1 & T2 (T1>T2) respectively.. The heat capacities of the source and the sink are equal. Find the final temperature attained.
  3. B

    Carnot efficiency vs thermal efficiency

    Is Carnot efficiency the same as thermal efficiency?
  4. schrodingerscat11

    Efficiency of Carnot engine that uses a paramagnetic substance

    Homework Statement Greetings! A Carnot engine uses a paramagnetic substance as its working substance. The equation of state is M = \frac{n D H}{T} where M is magnetization, H is the magnetic field, n is the number of moles, D is a constant determined by the type of substance, and...
  5. Kelsi_Jade

    Carnot Cycle Refrigerator - Thermal Battery Problem

    The question is: Consider a thermal battery - a device for storing mechanical energy. Use two large containers as heat reservoirs where one contains ice and water in equilibrium and the other contains steam and water in equilibrium. Both are held at pressure=1atm. Energy is stored by using a...
  6. 1

    Carnot Engine Question: Efficiency & Work/Heat Rejected

    Homework Statement A Carnot heat engine absorbs heat form a high-temp reservoir at 1200K and concerts some of it into useful work and rejects the rest to a low-temp reservoir at 400K. A) What is the efficiency of the engine? b) If the engine absorbs 2400J per cycle from the high-temp...
  7. Kelsi_Jade

    Find the work and heat transferred in a carnot cycle.

    I'm having some difficulty understanding how to find the work and heat transferred in a carnot cycle. Problem: One mole of ideal gas (cV=1.5 R) perform a Carnot cycle between the temperature 400 K and 300 K. On the upper isothermal transformation, the initial volume is 1 liter and the final...
  8. H

    Proving that a heat engine cannot exceed the carnot efficiency

    In many textbooks, a proof is provided where the work output of a super-efficient heat engine is provided to a carnot refrigerator, with the net result that a spontaneous heat transfer occurs from the cold reservoir to a hot reservoir. Let's use some numbers, TH = 600 K and TL = 300 K, so...
  9. fluidistic

    Carnot engine with a magnetic auxiliary system

    Homework Statement I would like some assistance to solve the following problem. A magnetic system satisfies Curie's law ##M=nDB/T##, has a specific heat capacity at constant magnetization ##C_M=\text{constant}##. It is used in a Carnot engine that operates between temperatures ##T_h## and...
  10. M

    Work of Carnot Engine integral

    I'm curious how do you choose the u and v transformations here to be equal to the constants and why is the f(u,v)=1 for the area- because you are summing infinitesimal x's and y's? I see that the area in xy is difficult to integrate because the sides are curved. is the transformation proven...
  11. A

    Published paper proving that Carnot efficiency can be exceeded

    I've theoretically proved that heat to work can be converted at 100% efficiency by proposing a system, named as the Blue system. And I've also proved that the entropy of the universe increases even if this system operates at 100% efficiency. The implication of this being that the Carnot theorem...
  12. B

    Carnot Cycle Graphs: Understand Work and Temperature

    Hello, In the Volume vs. pressure graph I understand the area under the curve is work. However, I have a hard time reconciling this graph with a pressure vs. temperature or a temperature vs. volume graph. What does the area inside the box represent? Work? Like which parts on the P vs. V graph...
  13. A

    Why is Carnot not irreversible?

    Hi, I am thinking about the Carnot-Cycle-Process. I know that a heat exchange is always irreversible. But in the Carnot-Cycle, there is heating too. Why is that kind of heating, in the Carnot-Process reversible? Thx Abby
  14. J

    Comp. Physics: Finite time Carnot cycle

    Hi, For my Bachelor's thesis I've been working on a finite time Carnot cycle. I've finished my numerical analysis using the differential equations governing the time evolution. My next step should be a simulation. First I should stick to a 1 dimensional system. This system consists of a...
  15. A

    Calculating Work in Isothermal Processes of Carnot Cycle

    Hallo, I read about thr Carnot-Cycle and got a problem. A->B: isothermal B->C: adiabatic C->D: isothermal D->A: adiabatic I want to understand how to calculate the work done in the isothermal processes. I have read: W_{AB}= T_{H}Nk\ln{(\frac{V_{A}}{V_{\text{B}}})}\\...
  16. W

    Comparing Carnot efficiency to Stirling efficiency

    Homework Statement In the problem, we were to derive work and heat for each leg of the cycle. Then we are asked: In the definition of the efficiency of this cycle, η =W Qpos , where Qpos is the total positive heat flow to the engine, what is the efficiency of the cycle when Th = 700K and Tc =...
  17. S

    Carnot heat engine - calculate work

    Using Carnot heat engine we connect two objects with the same mass m, specific heat capacities c. At the beginning the body 1 has temperature T_{1} and body 2 T_{2}. Calculate: a) How much mechanical work can this engine give? I tried like this, but i believe this is very wrong :(...
  18. D

    Carnot Engine Between Reservoirs with Varying Temperatures

    Homework Statement Two containers with fixed volume are each filled with n moles of a monatomic ideal gas with constant heat capacity. Initially, the volumes of gas are at temperatures T_1,i and T_2,i. What is the maximum amount of work that can be obtained by operating an engine between the...
  19. D

    Irreversible Carnot Vapor Power Cycle

    Two questions: 1. What does the T-s diagram look like for the irreversible cycle? 2. Do the isentropic efficiency equations that you apply to turbines and compressors (especially in the Rankine cycle) apply to the theoretical "turbines" and "pumps" in the Carnot cycle?
  20. V

    Efficiency of Carnot engine

    The problem: An engine puts an ideal monatomic gas through a clockwise rectangular cycle on a PV diagram with horizontal and vertical sides. The lower left point has a pressure of 1 atm and a volume of 1m^3 and the upper right point has pressure and volume three times greater. Calculate the...
  21. C

    Carnot Engine ~ Electric Generating station

    Homework Statement An electric generating station is designed to have an electric output power of 1.4 MW using a turbine with two-thirds efficiency of a Carnot engine. The Exhaust energy is transferred by heat to a cooling tower at 110°C. a) Find the rate at which the station exhausts energy...
  22. L

    Carnot Refrigerator Efficiency and Energy Calculations | Homework Help

    Homework Statement An ideal refrigerator utilizes a carnot cycle operating between 0 and 25 degrees celsius. To turn 10 kg of water at 0 degrees celsius into 10 kg of ice at 0 degrees celsius, a) how much heat is exhausted into the room? b) how much energy must be supplied to the...
  23. A

    Carnot Efficiency of a heat engine

    My problem only gives me joules to work with. Is it possible to convert from joules of energy to temperature (Kelvin)?? If so how?
  24. H

    Did Carnot use caloric theory .

    Did Carnot use "caloric theory". Wikipedia asserts the following: "Though Carnot had developed a compelling analysis of a generalised heat engine, he had employed the clumsy and already unfashionable caloric theory." http://en.wikipedia.org/wiki/Beno%C3%AEt_Paul_%C3%89mile_Clapeyron...
  25. M

    Why can no other engine be more efficient than a Carnot engine?

    Hello, I am having difficulty understanding the paragraph in my textbook explaining why no other engine can be more efficient than a carnot engine. What does it mean? To prove the validity of this theorem, imagine two heat engines operating between the same energy reservoirs. One is a Carnot...
  26. S

    [Thermodynamics] Two bodies exchanging heat through a Carnot engine

    Homework Statement It's basically the classic problem I've seen here a lot. There are two bodies, both with equal heat capacity (C_P), one at temperature T_1 and the other at T_2. They exchange heat using an infinitesimal-reversible Carnot Engine, which will work until thermal equilibrium is...
  27. S

    What is the efficiency of a Carnot engine and the effectiveness of a heat pump?

    Homework Statement 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...
  28. T

    Question about the Carnot engine

    I was reading about the Carnot engine, and I stumbled upon this forumla: Carnot efficiency = 1 - (QH-QL)/QH = 1 - (TH-TL)/TH Where QH is the heat input, QL is the heat output, TH is the input temperature, TL is the output temperature. The book says that TH is proportional to QH, and TL...
  29. D

    Carnot Cycle and Reversibility

    I'm trying to resolve some of my conceptual sticking points with the Carnot cycle. For one thing, I'm reading Reiss's Methods of Thermodynamics, and he offers a proof that the Carnot cycle obtains maximum efficiency when conducted reversibly. How can the cycle be conducted reversibly? During...
  30. S

    How did Carnot arrive at his theorem?

    The part of his theorem to which I am referring is the equation relating the heat & temperature for a reversible between temperature sources. QH / TH = - QC / TC Did he derive somehow from the forerunner equations of the ideal gas law (i.e., Charles & Boyle's Laws)? (He could not have taken...
  31. O

    Why Is My Calculation of Carnot Engine Efficiency Incorrect?

    Homework Statement A Carnot engine operates between 230°C and 120°C, absorbing 6.30*10^4 J per cycle at the higher temperature. What is the efficiency of the engine? Homework Equations eff = 1 - (Tcold/Thot) The Attempt at a Solution Using this equation, I get 47.83 percent...
  32. M

    Is the Carnot efficiency valid for fuel cells?

    So, I've read in books and on Wikipedia (see for instance http://en.wikipedia.org/wiki/Carnot%27s_theorem_%28thermodynamics%29#Applicability_to_fuel_cells_and_batteries) that the Carnot efficiency cannot be applied to a fuel cell because it is not a heat engine that produces work, operating...
  33. L

    Question regarding carnot cycle

    In Carnot cycle we assume that heat addition takes place at constant temperature(temperature of system and source being same) and same is the case for Heat rejection. But as we know that for heat flow (ie heat addition and heat rejection), temperature difference has to be there between system...
  34. D

    Heat Engine Carnot Efficiency question

    Homework Statement A heat engine has a carnot efficiency of 0.11. How much internal energy does this engine use in order to do 5.1 x 10^4 joules of work? How much heat does this engine give off/exhaust?Homework Equations (change in)U=Q-W W=(change in)E
  35. K

    Carnot engine efficiency * Carnot refrigerator efficiency

    Carnot engine efficiency is: \eta_{work} = 1 - \frac{T_c}{T_h} Carnot refrigeration efficiency is: \eta_{cool} = \frac{ T_c }{T_h-T_c} \eta_{cool} = \frac{ 1 }{\frac{T_h}{T_c} - 1} Simple multiplication should give me the efficiency where both the engine and the refrigeration share the...
  36. fluidistic

    Carnot cycle, fundamental equation of ideal gas

    Homework Statement Assuming that the auxiliary system in the Carnot cycle is a monoatomic ideal gas whose fundamental equation is S=\frac{NS_0}{N_0} +NR \ln \left [ \left ( \frac{U}{U_0} \right ) ^{3/2} \left ( \frac{V}{V_0} \right ) \left ( \frac{N}{N_0} \right ) ^{-5/2} \right ]. 1)Find...
  37. A

    Carnot Cycle: Exploring Heat Efficiency and Adiabatic Processes

    I have some trouble understanding the carnot cycle and why you have to make it so complicated, i.e. this process involves 2 isothermal and 2 adiabatic processes. If you want an engine with maximum efficiency why can't you just have a system whose temperature is just a tiny inch above your hot...
  38. O

    What's special about the Carnot Cycle?

    Why do we always talk about the Carnot cycle as being the most efficient, ideal engine? Doesn't the same equation hold for any reversible heat engine operating between two thermal reservoirs? Couldn't you prove e = 1-T_{L}/T_{H} for any reversible cycle? And then you can apply the usual "no...
  39. L

    Reverse Carnot - Refrigeration Cycle problem

    Hi guys, I have difficulties understanding the what I need to do in this problem. I have a ideal refrigeration cycle. first part is standard calculations, work of compressor and such. Results are Temperature range between -23 and 60 degrees C. Second part is the one that i do not understand. it...
  40. M

    Carnot Efficiency vs Rankine Efficiency

    Hi, Given value of top and bottom temperatures can anyone explain why the Ideal Carnot Cycle is more efficient than the Rankine cycle but why the Rankine is the preferred model? I know that in the Carnot the pump would have to be able to deal with a mixture of steam and water and the turbine...
  41. F

    Power of an Ideal Refrigerator - Carnot Engines

    Power of an Ideal Refrigerator -- Carnot Engines Homework Statement The inside of an ideal refrigerator is at a temperature T_c, while the heating coils on the back of the refrigerator are at a temperature T_h. Owing to a malfunctioning switch, the light bulb within the refrigerator remains...
  42. S

    Open System Carnot Efficiency

    Homework Statement The original is in German, but I will try my best to translate. A power generator uses the temperature difference between surface ocean temperature and sea bottom temperature (27C and 6C) to generate electricity. The power outage is 50kW at 10% of the Carnot efficiency...
  43. M

    Reversible Carnot Cycle and Heat Engine

    Homework Statement A borehole produces 120kg/s of high pressure water at 165°C. A powerplant is to be designed to extract heat from the water, reducing the temp to 147°C. The plant which will initially be assumed to be reversible, will reject heat at 17°C to a river. Take 147°C as the highest...
  44. S

    Carnot refrigerator and II law of Thermodynamics

    As per II law of thermodynamics you it is NOT possible that a hotter body becomes hotter and colder body becomes colder when in contact. But in a Carnot refrigerator, the heat is taken from a cold reservoir and pushed to a hotter one. It sort of opposite the II law. Help me over this paradoxical...
  45. P

    Carnot Engine refrigerator temp

    Homework Statement A Carnot engine is operated as a refrigerator, taking in 18 J of heat every second and expelling 20 J into a 23oC room. What is the temperature inside the refrigerator? a. 15.4oC b. 3.33oC c. -6.62 oC d. -15.4 oC Homework Equations e=1-T(cold)/T(hot) U=Q-W...
  46. S

    How Do You Calculate Efficiency in a Carnot Cycle Involving Argon?

    Homework Statement its part VI) of a big problem, where: 0.12 moles of argon (40) undergoes the cycle abca described in the graph. Process ab lies on a 540k isotherm. In the previious 5 sub problems, i figured that: Tc=270k Qbc=670J (lost) Qca=400J (added) Wab=370J Wabca=100J...
  47. A

    Carnot Cycle: Reversibility Under Constant External Pressure

    An ideal, monatomic gas is going through a 4 step Carnot cycle. Step 1 is an adiabatic expansion. Step 2 is an isothermal expansion. Step 3 is an adiabatic compression. Step 4 is an isothermal compression. The whole cycle is reversible. My question is how would the cycle change if step 1 is done...
  48. T

    Carnot Heat Engine: Solve for Heat Expelled to Cold Res.

    Homework Statement Consider a Carnot engine that operates between a hot reservoir at 63°C and a cold reservoir at -14°C. In running 25 minutes, this engine absorbs 590 J of heat from the hot reservoir. How much heat does it expel to the cold reservoir? Homework Equations Q_H/Q_C =...
  49. D

    Calculating Maximum Cycle Temperature in Carnot Cycle | Homework Solution

    Homework Statement An ideal engine operating on the Carnot cycle with a minimum temperature of 25°C develops 20 kW and rejects heat a rate of 12 kW. Calculate the maximum cycle temperature and the required heat supply of the cycle. Homework Equations Qhot/Thot =Qcold/Tcold...
  50. G

    Calculating Power plant's electric output in relation to carnot efficiency

    We were assigned a problem in class, but because it was on guest lecturer material, I am unclear of which given numbers and what equations to use. I do know I am supposed to use: η=TH-Tc/TH But I am confused as to why I have been given 4 variables ...Please Help! Here is the question [1] You...
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