Questions tagged [carnot-cycle]

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Why doesn't the heat in the two isochoric processes count towards efficiency calculation in Stirling cycle?

I'm trying to understand Stirling Cycle that consists of two isochoric processes and two isothermal processes. The heat transfer are given as $$Q_1 = \nu RT_1 \mathrm{ln} \frac{V_1}{V_2}$$ $$Q_2 = ...
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Carnot cycle restoration of original system state

In the Carnot cycle the original state is restored so there is no overall change in entropy. Why is it not possible to accomplish this simply with two reversible isothermal steps, the first an ...
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Derive the Carnot Efficiency without using the Carnot Cycle? [closed]

How can you derive the Carnot efficiency using only properties of reversible cycles?
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Is there only one Carnot cycle for every thermodynamic system?

So, Carnot engine is THE reversible engine operating on two reservoirs. No other engine can beat its efficiency on two reservoirs (eg. Otto cycle is not Carnot as it requires infinite number of ...
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Are there actual technical realizations of the Carnot cycle?

The Carnot cycle is composed of four steps: isothermal expansion, adiabatic expansion, isothermal compression and adiabatic compression. In the case of combustion engines, we have the idealized Otto ...
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Is my interpretation of how a Carnot Cycle works correct?

I'm trying to understand how the Carnot cycle works in my learning of it. Here's what I so far believe is what is happening: (A $\to$ B) A cylinder of gas is connected to a frictionless piston, and ...
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1answer
974 views

Does Piston moves faster when we accelerate the car?

I am learning about car basics. I found that engine is nothing but a system where heat energy is converted into up/down motion of the piston in the cylinder. Finally, this up/down motion is converted ...
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206 views

About the 2nd Carnot Corollary

I have a question about the 2nd Carnot Corollary. According to Moran, Fundamentals of Engineering Thermodynamics, the 2nd Carnot Corollary stated that "all reversible power cycles operating between ...
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1answer
110 views

Does a Carnot-efficient heat engine recover all work that was initially done?

There are two adiabatic containers filled with an ideal gas. In container A work is done which eventually turns completely into heat, leading to a temperature difference between container A and ...
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152 views

Cascade Carnot cycle

In a Carnot cycle about 50% of the energy is converted in work whereas the other is dissipated in heat to the heat sources. Is it possible to reuse the heat in another cycle to reconvert 50% of it ...
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Confusion about Clausius inequality

I am trying to learn the derivation of Clausius inequality in the following manner. Consider the following diagram "Reversible cyclic device" is working in Carnot's cycle. The combined system gets ...
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1answer
99 views

Reverse the combustion engine

All you know what a combustion engine is doing: Transform chemical energy into kinetic energy. What about the opposite? I know when I park a car at a slope and lose the breaks it will drive ...
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1answer
127 views

Carnot cycle with varying reservoirs

I was thinking what will happen to the standard Carnot cycle, if instead of - say - the usual cold reservoir, we adopt a smaller refrigerator, whose temperature in fact changes after the heat release ...
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Efficiency of a thermodynamic cycle

We are given a thermodynamic cycle of an ideal gas (but of rigid spheres) composed of a single substance which undergoes a Carnot cycle illustrated below. All processes are assumed to be reversible. ...
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362 views

Irreversible processes don't account in entropy calculations?

Pick a Carnot Cycle (being $T_1<T_2$), it is reversible, therefore $\Delta S_{univ, cycle}=0$. The same result is obtained via the sum of all entropies associated with its transformation, which ...
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382 views

Where does the energy come from for adiabatic processes of a Carnot cycle?

I'm getting stuck on where this additional energy comes to move the piston further outward/inward during adiabatic processes when the only energy changed is during isothermal processes. Can someone ...
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Is existence of incompressible bodies prohibited by Carnot's theorem and Clausius' inequality?

Consider an absolutely incompressible body, which does not change its volume $V$ under pressure $p$ but can expand or shrink when its temperature $T$ changes. Then its equation of state has a simple ...
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291 views

Is “entropy” not a state variable for irreversible process?

Any reversible process can be described as a sum of many infinitesimally small Carnot cycles, so $\oint {dS} = \oint {\frac{{dQ}}{T}} = 0 % MathType!MTEF!2!1!+- % ...
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Confusion about forces in the work done on the piston by the gas in Carnot cycle

I was drawing a free body diagram of the 3rd step of the Carnot cycle as shown below. The forces with - sign are reaction forces to the forces without the sign, according to Newton's 3rd law of ...
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How to prove that an arbitrary cycle in the PV diagram has an efficiency less or equal than Carnot's Cycle? [duplicate]

The statement is: Consider an ideal gas with constant number of particles (N is constant), and an arbitrary thermodynamic cycle (closed curve with no self-interesections) in the PV diagram. Show that ...
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1answer
4k views

Calculating the maximum efficiency of an engine cycle

I'm a little confused about calculating the maximum efficiency of an engine cycle. From what I've learned the carnot cycle is connected by two adiabatic processes and two isothermal, and this is the ...
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151 views

Why does a system expand isothermally?

Considering the first step of the Carnot process, heat is transferred from a bath to the system with both at the same temperature. But how does this process start? Why should the system spontaneously ...
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80 views

Müser engine and solar conversion efficiency

I found in many reference a derivation of the maximal conversion efficiency from solar power to work with the so-called that I found dubious (see for instance here). It usually goes like this. Let us ...
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1answer
558 views

Is Carnot's theorem equivalent to the Second Law of Thermodynamics?

In thermodynamics we have Carnot's Theorem which states that the efficency of any heat engine wich works with only two temperature's source is less or equal to Carnot's engine which works between the ...
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Distributed Workload AS cooling?

To my understanding, many processes require cooling to achieve optimum use. Power stations, for example, require cooling for electricity production. Computer hardware systems, similarly require ...
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380 views

optimality of the Carnot cycle

It is well-known and is stated always and everywhere that the Carnot cycle is the most efficient thermodynamic cycle. Although stated as such it is rarely proven. One proof is in the article "Engine ...
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Why is the efficiency of a carnot engine maximum?

I know carnot engine consists of isothermal and adiabatic process. My question is why the efficiency of carnot engine is maximum? Why not it is maximum with other processes. In one book I read ...
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Understanding why $\int_{T_1}^{T_2}C_Vd\ln(T) + \int_{V_1}^{V_2} nRd\ln(V) = 0$ is violated when $T_2$ and $V_2$ are picked

In Chapter 4 of Chemical Thermodynamics, by Peter A. Rock published by Oxford University Press, 1983, the author is trying to explain why a new state function is needed, specifically a state function ...
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Difference between reversible and irreversible adiabatic process in PV diagram

let's say we've got a carnot-cycle in a pressure volume diagram with the following processes: 1 -> 2: reversible isothermal 2 -> 3: reversible adiabatic 3 -> 4: reversible isothermal 4 -> 1: ...
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Why is the cyclic volume integral of $P/T$ larger than the one of $P_ext/T$ in an irreversible process?

In order to derive the Clasius inequality we can call the first law of thermodynamics in it's differential form: $$dU={\itđ}q-P_{ext}dV.$$ If the process is reversible: $$dU={\itđ}q_{rev}-PdV.$$ ...
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Why can't we make Carnot heat engine in real life?

Question is obvious: Why can't we make Carnot heat engine in real life? I read Wikipedia and Fundamentals of Physics (Halliday) but I didn't found anything about my question. there we're explanations ...
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182 views

Question about air-conditioning cycle

All explanations of the air-conditioning cycle are somewhat like this: https://www.swtc.edu/ag_power/air_conditioning/lecture/basic_cycle.htm My question is... how do we ensure the refrigerant is in ...
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Carnot cycle modelization

In some sources, there's a slight difference in the Carnot cycle stages description. Let's take the "first" - the isothermal expansion. Some say that as a consequence of the contact between the ...
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How to make sense of paradoxical heat pump?

Here is the paradoxical situation. Suppose you have two objects at temperatures $T_1$ and $T_2$, where $T_2>T_1$. Also, suppose you have some work at your disposal to power a heat pump whose ...
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1answer
4k views

Final temperature after maximum work output?

Two simple identical blocks with heat capacity $C$ are at temperatures $T_2$ and $T_1$ respectively, with $T_2>T_1$. What is the final temperature of the two blocks if the maximum possible work is ...
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The Carnot engine and entropy?

The Clausius statement of the second law of thermodynamics is as given below: "Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the ...
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Why doesn't the water cycle stop, since it dissipates energy?

In artificial cycles like for example refrigeration cycle, because of irreversibilities extra energy is require to be provided so that the refrigerant is available at the same state as it was at the ...
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477 views

How is Carnot's theorem valid also for engines that are not heat engines?

I understood the statement and the proof of the Carnot theorem. Carnot's theorem states: All heat engines between two heat reservoirs are less efficient than a Carnot heat engine operating ...
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573 views

How do you calculate the efficiency of a steam turbine?

Yesterday I saw a comment on an article that claimed a turbine with a steam temperature of 500° F and a room temperature 70 ° F couldn't possibly have an efficiency higher than 45%. He used the carnot ...
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1answer
71 views

What does the ratio of reservoir temperatures have to do with the efficiency of a heat engine?

I am having a conceptual difficulty with heat engine efficiency. I do not understand why having a larger difference in temperature between the hot and cold reservoirs have an effect on the thermal ...
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1answer
816 views

Application of Carnot's theorem to calculate efficiency of thermal engine

I understood Carnot's theorem in theory, but I still have some doubt on the practical use of it. In particular I would like to know: if I have any reversible cycle followed by a gas, then the thermal ...
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Does the thermal efficiency depend on the reversibility of the engine when isochoric or isobaric processes are involved?

I'm confused on the efficiency of a thermal engine (with an ideal gas) in the case in which it is reversible or not reversible, in particular where the ideal gas follows isochoric or isobaric ...
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Heat Pumps and COP?

Heat Pump COP (Coefficient of Performance) $$COP=1-\frac{T_c}{T_H}$$ With Heat Pumps is the efficiency/COP more dependent on the hot or the cold reservoir and why?
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Why is the efficiency of human cells less than the efficiency of an Otto engine?

I always used to think (I don’t know why!) that the efficiency of human (and animal and plant) cells should be equal to or near the efficiency of a Carnot engine or at least should be the highest ...
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222 views

Entropy and Clausius inequality

From the Clausius inequality we can derive that the efficiency of a Carnot (reversible) cycle is given by: $$e= 1 - \frac{T_c}{T_h}$$ Is this true for every reversible cycle? Is the efficiency of all ...
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2nd law of thermodynamics' violation?

According to 2nd law of thermodynamics, it is not possible to convert heat 100% into work. Well, investigating about the Carnot Cycle, I have found out that in the first step, the process is to heat ...
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107 views

Carnot engine basics?

A line in my textbook says.. ' if we employ any other process that is not adiabatic, say an isochoric process, to take the system from one temperature to another, we shall need a series of ...
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A system with temp T is in contact with a reservoir of temp T. Would the system ever take in energy and expand (do work) in this situation?

The context is explain a Carnot cycle and how to get work from a system. Its starts by saying the system is in equilibrium with its surroundings, but then it take in some energy Qin. How does ...
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Example of a Carnot machine made of a different physical system than a ideal gas?

Anybody knows an example of a Carnot machine made with any different thing than a gas? For example wire or a magnet. I was wondering that since I read the Kardar's book on Statistical Mechanics. He ...
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Carnot Engine- Cold Reservoir is a black body [closed]

My question: A satellite powered by a Carnot engine uses heat from a nuclear reactor at a fixed temperature T0. Heat is released into outer space via thermal radiation emitted by a set of fins at ...