# What is Carnot engine: Definition and 106 Discussions

A Carnot heat engine is a theoretical engine that operates on the Carnot cycle. The basic model for this engine was developed by Nicolas Léonard Sadi Carnot in 1824. The Carnot engine model was graphically expanded by Benoît Paul Émile Clapeyron in 1834 and mathematically explored by Rudolf Clausius in 1857, work that led to the fundamental thermodynamic concept of entropy.
Every thermodynamic system exists in a particular state. A thermodynamic cycle occurs when a system is taken through a series of different states, and finally returned to its initial state. In the process of going through this cycle, the system may perform work on its surroundings, thereby acting as a heat engine.
A heat engine acts by transferring energy from a warm region to a cool region of space and, in the process, converting some of that energy to mechanical work. The cycle may also be reversed. The system may be worked upon by an external force, and in the process, it can transfer thermal energy from a cooler system to a warmer one, thereby acting as a refrigerator or heat pump rather than a heat engine.

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1. ### B Question regarding Heat Transfer in Carnot Engine

***A Carnot Engine*** is a theoretical engine unlike a Sterling Engine which can be made practically. Some of the drawbacks of Carnot Engine are, 1)The Heat Transfer occurs only during isothermal process(compression and expansion),this is because the working material (ie) gas or fuel used, if...
2. ### Net efficiency of a cascaded Carnot Engine and Fridge

Here is a diagram of my interpretation of the problem: Where I'm thinking that the engine originally takes heat from ##T_h## to ##T_l##, in which case ## \frac { Q_{h} } { T_{h} } = \frac { Q_{l} } { T_{l} } ## and ## W_{out} = Q_{in} - Q_{out} = Q_h \left( 1 - \frac {T_l} {T_h} \right) ##...
3. ### A Carnot engine between the Earth's poles and equator

Earth absorbs and releases a massive amount of energy as a part of the day night cycles.(~100 Peta watts of solar radiation received) And the temperature difference between the poles and equator drive weather phenomenon, which happens at an energy scale beyond technology. I am wondering if one...
4. ### Calculating the waste heat of Carnot engine

The answer is 6470 J. So since I have the two temperatures I could calculate the efficiency. First I convert to kelvin then get an efficiency of 0.35481. Now I can use e=W/Qin to get Qin. I get a value of 10033.54J. Now I can use e=(Qin-Qout)/Qout to get Qout, the waste heat. I get 7405.9 J...
5. ### Carnot engine physics question

Homework Statement: In a well-insulated refrigeration unit, a Carnot engine using an ideal gas is driven by a 1KW electric motor (80% efficient) to freeze water. Assuming that the temperature of the thermal sink is 20 °C, calculate the mass of water frozen in 5 minutes. Take the latent heat of...
6. ### Can we make electricity from heat?

I am a refrigeration technician with a fascination for heat pumps. I wonder if we can make two systems in parallel. The Carnot heat engine is used to describe the steam locomotive. I want to use a different fluid with a lower boiling point to create a heat engine using a refrigeration cycle...
7. ### Efficiency of a steam power plant

My inital assumption was to just take T1 = 5600 and T2= 300K, find the maximum efficiency and then divide it by two and three but I don't believe this question to be that simple. I'm confused as to where the 750K fits in as I thought no matter what occurred in between the heat reservoir and heat...
8. ### Calculating work done by a Carnot engine

"A Carnot engine operates using a heat source at 500 °C, and a heat sink at room temperature (20 °C). Suppose that as a heat source, you use the combustion of 100 cubic feet of natural gas at room temperature and pressure (e.g. in a fuel cell of some kind). Under ideal conditions, what is the...
9. ### Maximum work done by a Carnot engine

Homework Statement Homework EquationsThe Attempt at a SolutionTaking the engine to be a Carnot engine, ## \eta = \frac { T_h – T_c } {T_h} = \frac { W} {Q_h} ## ...(1) ## Q_h = C(T_h – T_f) ...(2) \\ Q_c = C(T_f – T_c) ...(3) \\ W = Q_h – Q_c = C(T_h + T_c – 2 T_f) ## ...(4)Solving...
10. ### Overall efficiency of cascaded reverse Carnot engine & a Rankine turbine

Assuming a reverse Carnot engine (Heat Pump Achieve 353K after compression and 253K after evaporation) is cascaded to Rankine turbine such that heat rejection to a steam boiler and heat is collected from a thermally isolated compartment first (used as condensation by cooling) then from ambient...
11. ### Temperature in a Carnot heat engine

Homework Statement A Carnot heat engine takes 95 cycles to lift a 10 kg. mass a height of 11 m . The engine exhausts 14 J of heat per cycle to a cold reservoir at 0∘C. What is the temperature of the hot reservoir? Homework Equations η=1-(Tc/Th)=W/Qh The Attempt at a Solution I've tried...
12. ### Proving Carnot efficiency is maximum and conditions

The standard proof to show carnot efficiency cannot be exceeded is to couple a supposedly more efficient engine to a carnot refrigerator, and show that it would violate second law. However, isn't it true that we can make the same argument with any arbitrary efficiency? Some discussions on...
13. ### Carnot Engine cycle on PV Diagram

I posted this in the engineer / comp science thread, but I've had no one reply or help. I really could use some guidance and I don't know where else to post. Homework Statement I am tasked to create a PV Diagram of a Carnot Engine Cycle. I must find pressure, volume, Q, W, ΔU, and ΔS on all...
14. ### Plotting Carnot Engine Cycle on PV Diagram

Homework Statement I am tasked to create a PV Diagram of a Carnot Engine Cycle. I must find pressure, volume, Q, W, ΔU, and ΔS on all four points. This is what has been given to me by my teacher: a to b : Isothermal b to c: Adiabatic c to d: Isothermal d to a: Adiabatic TC = 300 K TH = 1700 K...
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### Work done by a Carnot Engine. Melting ice

Homework Statement The problem is that a Carnot contains Boiling water in the hot reservoir and ice water in the cold reservoir. Given that 0.0400kg of ice is melted in 5 minutes, what is the amount of work done by the engine. Homework Equations Qh/Qc=Th/Tc W=Qh-Qc W=(1-Tc/Th)Qs q=mHf...
16. ### Carnot engine efficiency problem

Homework Statement A Carnot engine absorbed 1.0 kJ of heat at 300 K, and exhausted 400 J of heat at the end of the cycle. What is the temperature at the end of the cycle? Homework Equations The efficiency of a Carnot engine is given by the formula Efficiency = 1 – Qc/Qh = 1 –...
17. ### How to show that Carnot engine is more efficient?

Homework Statement Consider an Ideal gas engine with the following cycle: i. Isobaric expansion (T1 -> Th) ii. adiabatic expansion (Th -> T2) iii. Isobaric compression (T2 -> T_L) iv. adiabatic compression (T_L -> T1) a. Find its efficiency b. When operated in two temperature, show that Carnot...
18. ### What is the difference between Otto engine and Carnot engine

What is the key difference between Otto engine and Carnot engine? Other than it is reversible or not, it seems to me they are so similar. Thanks.
19. ### Carnot engine acting upon another Carnot engine

Homework Statement Suppose an amount of power P_{\ell} is delivered to a load by a black box with potential difference V_T across it, driving current I through a single loop. If an amount of power P_b is applied to the black box, to sustain I at V_T, then the efficiency of this black box acting...
20. ### What is the Temperature of the Low Temperature Reservoir in a Carnot Engine?

Homework Statement A Carnot engine moves a piston which applies 5N of force to a rotating disc by moving a piston 0.25cm for a total of 5W of power. If the high temperature reservoir is 100K, what must the temperature of the low temperature reservoir be? Homework Equations The efficiency of a...
21. ### Does efficiency always depend on reversibility of the engine?

I'm confused on the efficiency of a Thermal engine in the case it is reversible or not reversible, in particular where the ideal gas follows isochoric or isobaric processes. Infact during isochoric and isobaric processes $$Q_{isochoric}=n c_v \Delta T$$ $$Q_{isobaric}=n c_p \Delta T$$ So the...
22. ### Thermodynamics - Heat engines

My question is: according to Carnot cycle, the maximum efficiency of a heat engine is given by 1 - T2/T1, where T2 is the temperature of the cold source and T1 the temperature of the hot source. So, accordingly, as higher T2 is for a same T1, lowest is the efficiency of the engine. But, the...
23. ### Heat Extracted and Delivered to Reservoirs in a Heat Engine

NO TEMPLATE---MISPLACED HOMEWORK So it seems like a pretty simple question, and in all likelihood it is, but my lecturer somehow managed to miss this bit in his lecture notes. A heat engine operates between 500K and 300K with 20% of the efficiency of Carnot engine operating between the same...
24. ### Thermal Question -- Carnot Engine

Homework Statement A Carnot engine extracts 745 J from a 592-K reservoir during each cycle and rejects 485J to a cool reservoir. It operates 16 cycles per second. Find work, efficient, temp of cool reservoir. Homework Equations W = Qh - Qc n=Wout/QhThe Attempt at a Solution I'm sure I can do...
25. ### Help with thermodynamics -- work of Carnot engine expansion

Homework Statement I don't need help solving I just need some clarification. Since the carnot cycle is adiabatic, the first law would reduce to work= mass*(change in internal energy). On my test I was asked to calculate the work of the isentropic expansion of a carnot engine with air...
26. ### Efficiency of a Carnot Engine

The efficiency of a Carnot Engine is described by the relationship: Tc/Th = Qc/Qh, so that e(Carnot) = 1 - Tc/Th For heat engines, can their efficiency also be related to temperature as well? Or is the description of their efficiency just: e(heat engine) = W / Qh = 1 - Qc/Qh I am inclined to...
27. ### Exploring Alternatives to the Carnot Engine

1 - T1/T2 gives efficiency of a carnot engine working between two temperature sources T1 &T2 and we know that, that efficiency is unbeatable but can there be another engine possible serving the same purpose as that of carnot engine working in an entirely different manner and MORE EFFICIENT than...
28. ### The efficiency of a Carnot engine

I can't realize the proving why Carnot engine has the highest efficiency. "Let εc be the efficiency of a Carnot engine operating between two given temperatures.If an engine X, which has an efficiency εx that is greater than εc.We can couple engine X to a Carnot refrigerator , and they make a...
29. ### Thermodynamics-reversible carnot engine

Homework Statement a refrigerator is used to convert 1 kg of liquid water at 30 degree celsius to ice at -18 degree celsius.the refrigerator rejects heat to surroundings which are at 30 degree celsius.the specific heat values of liquid water and ice are 4.18 kj/kgk and 1.9 kj/kgk respectively...
30. ### Confused about the Carnot engine?

I am teaching myself thermodynamics (and really enjoying it!) but am slightly confused about Carnot's engine. From the equation efficiency=1-T(cold reservoir)/T(hot reservoir), I see that the most efficient engine is one where the difference in temperature between the cold and hot reservoirs is...
31. ### Is Carnot engine the only reversible engine?

Is Carnot engine the only form of reversible engine? Is it possible to have a different form of reversible engine that goes through different processes? For a standard Otto cycle working with ideal gas, theoretically the two processes involving isochoric pressure change can be reversible...
32. ### Carnot Engine heat delivery

Homework Statement A Carnot engine uses a hot reservoir consisting of a large amount of boiling water and a cold reservoir consisting of a large tub of ice and water. When 6437 J of heat is put into the engine and the engine produces work, how many kilograms of ice in the tub are melted due to...
33. ### A Carnot engine using methane

Homework Statement A Carnot engine operates with 1 kg of methane, which we will consider an ideal gas. The ratio of specific heat capacities \gamma is 1.35. The ratio of maximum volume to minimum volume is 4 and the cycle efficiency is 25%. Find the entropy increase during the...
34. ### Carnot Engine with finite reservoirs

Homework Statement A Carnot engine operates between two finite heat reservoirs of total heat capacity CtH and CtC. a) Develop an expression relating TH to TC at any time. b) Determine an expression for the work obtained as a function of CtH ,CtC , TH and initial temperatures TH0 and TC0...
35. ### Heat Efficiency of a Carnot Engine

Homework Statement A Carnot engine operates between a warmer reservoir at a temperature T1 and a cooler reservoir at a temperature T2. It is found that increasing the temperature of the warmer reservoir by a factor of 2.00 while keeping the same temperature for the cooler reservoir increases...
36. ### Solar cells and 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...
37. ### 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.
38. ### 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...
39. ### 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...
40. ### 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...
41. ### 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...
42. ### 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...
43. ### 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...
44. ### 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...
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### 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...
46. ### [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...
47. ### 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...
48. ### 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...
49. ### 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...
50. ### 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...