Questions tagged [carnot-cycle]

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What does “entropy” really mean?

I'm currently taking a course of introduction to biophysics in college and we currently covered a subject called entropy (S). We did some maths based on the Carnot cycle and came up with the following ...
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Meaning of “Heat engine working between two Temperatures”

According to Carnot Theorem: "Of all engines working between two given temperature, none is more efficient than a carnot engine." I want to know what actually is meant by an engine working ...
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Theoretical efficiency of a laser

A laser produces a coherent, collimated light beam. This is like a less-disordered version of the light from say a light bulb. When I learned about heat pumps in thermodynamics class, I found that we ...
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1answer
27 views

$p$-$V$ Diagram of a real chiller (fridge, heat pump, …)

I am struggling to find a $p$-$V$ Diagram of a real (not CARNOT!) heat pump. Regarding engines (diesel, otto) this seems to be an easy task but I am failing to do so for heat pumps. Could anyone help ...
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1answer
25 views

Carnot cycle total reversibility

I read the discussion of the same problem in another problem posted here Carnot Total Reversibility, but still I can't get the reason why Carnot cycle is stated as "Totally Reversible", it ...
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1answer
26 views

Adiabatic expansion vs. adiabatic compression in Carnot cycle

I am currently studying the Carnot cycle, and am close to understanding it, but something is nagging on my mind. So, during the expansion process of the cycle, work is done on the surroundings as heat ...
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2answers
101 views

Is Carnot cycle the only “most efficient” cycle? [duplicate]

In all the books, that I have studied so far, they say that Carnot cycle is the most efficient cycle. But why isn't any other reversible process as efficient as Carnot cycle? Can somebody please ...
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105 views

Confusion with Carnot Cycle Problem

Consider two fluids $F_1$ and $F_2$ with equal volume and heat capacity as well as $T_1$ and $T_2$ respectively, whereby $T_1 > T_2$. One uses a Carnot cycle to transfer heat from $F_1$ to $F_2$ in ...
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1answer
30 views

Why Doesn't Thermal Radiation Render Thermionic Conversion Unable To Approach Carnot Efficiency?

Thermionic Conversion follows the classic Richardson-Dushmann Equation for thermionic current as a function of temperature squared: $$J_{RD} = A_0 T^2 \exp\left(-\frac{\phi}{k_B T}\right)$$ where $J_{...
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1answer
78 views

Why does adiabatic contraction bring Carnot engine back to initial state? (and other questions)

I have many questions (all in bold) around the Carnot cycle. I know I'm not the first one to ask a bunch of questions in the middle of a description of my own understanding, but having read other ...
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1answer
67 views

Why does $\oint\frac{\delta Q}{T} = 0$ when evaluated over a Carnot cycle?

In my thermodynamics schoolbook, it is asked to apply the Clausius inequality to a Carnot cycle. According to the book the answer is to evaluate $\oint\frac{\delta Q}{T}$ over the cycle which should ...
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1answer
74 views

Carnot heat engine at maximum power

I am trying to prove that the Carnot efficiency for a heat engine with maximum power is $1-\sqrt{\frac{\tau_l}{\tau_h}}$, where $\tau_h$ is the high temperature, $\tau_2$ the lower temperature, and we ...
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1answer
40 views

How to find efficiency of a cycle thats not Carnot Cycle?

Here is the Full Question: A monoatomic gas is expanded adiabatically from volume $V_0$ to $2V_0$ and then is brought back to the initial state through an isothermal and isochoric process respectively....
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1answer
36 views

Why is this equation valid in the carnot cycle? [closed]

I'm following a derivation here of a carnot-cycle and I'm stuck at $ T_3 / T_1 = T_4 / T_1 = (V_1 / V_4)^{(κ - 1)} = T_3 / T_2 = (V_2 / V_3)^{(κ - 1)} $ I don't get that. Is that due to ...
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56 views

Carnot cycle doubt

I am trying to solve a carnot cycle numerical, where I encountered a concept doubt. When heat is absorbed from the heat source/higher reservoir during first isothermal expansion, does the temperature ...
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1answer
288 views

Isothermal irreversible expansion of ideal gas

I am studying Thermodynamics in my first year and I don't quite understand the process of isothermal reversible/irreversible expansion. Below is a P-V graph I found on Google, just to help me ...
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0answers
33 views

How to explain from the second law that absolute zero cannot be attained?

How can we explain from thermodynamics that the absolute zero of temperature cannot be attained? I was thinking along the following lines. The efficiency of Carnot engine $\eta=1-\frac{Q_2}{Q_1}=1-\...
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1answer
112 views

Proof for $\oint \frac{dQ}{T}=0 $ in a reversible process

I'm actually trying to prove that Entropy is a state function. I get struck at the point where I need to prove that $\oint \frac{dQ}{T}=0 $ for a reversible process. Clausius in his book The ...
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2answers
433 views

How can we show that Entropy is a State Function?

Intro: Thank you for reading. I know there are lots of questions on Stack Exchange about entropy. The following is the one that most closely addressed my confusion: Entropy as a state property ...
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3answers
668 views

Why only isothermal and adiabatic for Carnot engine?

What is the reason behind choosing adiabatic and isothermal process for carnot engine? My book states the following reason. I am not able to understand it. It would be great if you could put it in ...
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1answer
84 views

In the isothermal expansion phase of a Carnot cycle, why does the gas expand?

Descriptions of the isothermal expansion in a Carnot cycle typically say heat is absorbed by the gas and the gas expands. But why would it expand? The heat reservoir keeps the temperature constant, ...
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1answer
34 views

The reversible Carnot cycle is the most efficient between $T_2$ and $T_1$. Is it a form the second law itself?

The second law of thermodynamics proposed by Clausius, Kelvin, Carnot ..etc in its original form as T dS> dQ for irreversible process and Tds =dQ only for reversible thermodynamics process. This ...
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2answers
50 views

Apparent contradiction concerning the net work of a Carnot cycle

The net work of a Carnot cycle, $W$, is $$\tag{1}W=Q_{h}-Q_c.$$ This work also satisfies $$\tag{2}W=Q_{h}\bigg ( 1-\frac{T_c}{T_h} \bigg )$$ Let us fix $Q_{h}$, the amount of heat initially ...
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2answers
33 views

Deriving $Q_{1}-Q_{2}=W$ for a perfect gas that had gone through a Carnot cycle

I saw multiple times that if an engine, say Carnot engine, absorbs heat $Q_{1}$ at $T_{1}$, does work $W$, and expels heat $Q_{2}$ at $T_{2}$, then we should have$$\tag{1}Q_{1}-Q_{2}=W.$$ Let us say ...
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83 views

How do I use calculus of variations to prove that Carnot cycle is the most efficient one?

There are already many questions on Physics SE asking for a proof of the maximum possible efficiency of Carnot's engine. However, none of them (at least the ones which I looked up) contain a ...
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2answers
47 views

Why does the gas compress during isothermal compression, in the carnot cycle

In this step, the gas is said to release some heat dq. From where does energy come from? The temperatures are the same, so internal energy won't flow. But the gas compresses, hence the change in ...
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48 views

About the adiabatic stroke in the Carnot cycle

I understood that in the adiabatic stroke, the internal energy is being used up to do work Again, assuming that the internal energy of all the gas molecules of the system are the same (can we?) Why ...
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1answer
152 views

Can anyone prove this overstated-but-almost-never-justified fact from thermodynamics?

Clausius inequality states that $\oint {\delta Q\over T}$ equals zero for a system undergoing a reversible cycle, whereas it can’t be greater than zero for an irreversible cycle. But everywhere, I ...
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1answer
78 views

Efficiency of heat engines

I have been taught that the an engine running on the Carnot's cycle has the maximum energy among the maximum efficiency, however I never found a convincing proof for it. Wherever I have put this ...
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1answer
56 views

Efficiency of sequential Carnot engines [closed]

A Carnot engine A operates between temperature $T_1$ and $T_2$ ($T_1>T_2$). A second Carnot engine B uses all the heat rejected by A as input and input and operates between temperature $T_2$ and $...
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0answers
41 views

Why an ideal gas expands in the 2nd step of carnot's cycle/engine?

In the 2nd step of carnot's cycle, when the gas cylinder is kept under an adiabatic condition, it expands and the temperature falls. My question is why does the gas spend it's internal energy to ...
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1answer
146 views

Efficiency of a reversible thermodinamic cycle

1 mole of ideal monoatomic gas completes a reversible ABC cycle, in which AB is a VOlume constant tranformation, BC an adiabatic expansion(Q=0) and CA an isotherm(Temperature during tranformation is ...
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2answers
179 views

Efficiency of Carnot engine [duplicate]

Why is the efficiency of Carnot engine regarded as the maximum efficiency possible for a heat engine?
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1answer
187 views

How does the Carnot Cycle work?

I am learning the Carnot cycle, which consists of four transformations for a fluid. In the first two transformations the volume of the fluid expands, generating work. This happens in two steps: ...
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2answers
425 views

Why is the Peltier / Seebeck Effect's efficiency so low in practical devices?

Usually solid state devices are able to attain excellent efficiency. However, currently existing Peltier coolers and Seebeck generators have horrible efficiency -- far worse than Carnot, and also far ...
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2answers
81 views

Thermodynamics problems with a cycle (insufficient data?)

I am having some troubles in solving the following problem a professor gave us, and in my opinion I think that either there are insufficient data or the solutions are infinite. We have a perfect gas,...
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2answers
151 views

Why a reversible engine's efficiency must be equal to that of a Carnot engine

Apparently, in order to prove that an engine must be as efficient as a Carnot engine if reversible is because apparently for its efficiency in either direction: $\eta_E \le (1-T_2/T_1)$ $\eta_R \ge (...
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1answer
64 views

Clausius's Carnot Cycle Equation Derivation

In his paper clausius describes a Carnot cycle and he continue arguing like below: In order to make an analytical application of the method...we will assume that all the changes which the gas ...
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3answers
414 views

Why is there Net Work Done on a Pressure/Volume Cycle?

The area enclosed by the rectangle is said to be the Net Work Done. My question is why would there be any net workdone if it returns to its initial position (W). Shouldn't it act like a force-...
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1answer
354 views

Can you calculate the supplied heat given a p(V) - Diagram of a isobar process?

You are given an p(V) - Diagram like this: Source: How to calculate the efficiency from a $p$-$v$ diagram? There you see two isothermal processes and two isochor processes. For every given ...
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2answers
575 views

Why does there need to be an isothermal compression in a Carnot cycle?

This is the part that allows the Carnot engine to not violate the 2nd law of thermodynamics, but, hypothetically, why can't we just adiabatically compress the working substance to get it back to State ...
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1answer
408 views

Why is there a cold reservoir in a Carnot engine?

I'm trying to wrap my head around the idea behind a Carnot engine. The main question I'm trying to figure out is how a Carnot engine actually works in producing work. I'll provide a picture for ...
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1answer
49 views

Deriving the second law of thermodynamics from an irreversible carnot process

I have studied the ideal carnot cycle extensively where we assume that $$\Delta S_{\mathrm{total}}=\sum_i \frac{Q_i}{T_i} =0$$ Now I was wondering whether it is possible to derive basic properties ...
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1answer
112 views

Limitations of converting pressure into kinetic energy

Bernoulli's principle states that an increase in the kinetic energy of a fluid occurs simultaneously with a decrease in pressure for isentropic processes. What then limits us from converting all of ...
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2answers
716 views

How do I prove that the Carnot cycle is the most efficient graphically? [closed]

I have to prove that the Carnot cycle is the most efficient by comparing it with a arbitrary cycle working within the temperature range of $T_L$ to $T_H$ in a ST-diagram. How do I do this?
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1answer
63 views

Entropy generation in an endoreversible engine

An endoreversible engine is one that is internally reversible (i.e., a perfect Carnot engine) but the heat transfers occur across imperfect conductors (resistances), thus rendering the engine ...
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2answers
307 views

How is the work done by Carnot Engine obtained or converted to usable form?

I read about the Carnot Cycle and Carnot engine where it was said that the work done by this engine is equal to the area enclosed in the PV diagram. I understood the proof and everything but I am not ...
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1answer
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Efficiency of a Carnot machine, in which, some of its extreme points are in the region of liquid transition to steam

I need to calculate the efficiency of a Carnot machine, in which, some of its extreme points are in the region of liquid transition to steam with the works, differences of energy and heats of each ...
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1answer
144 views

Carnot's Engine Proof flawed?

https://www.youtube.com/watch?v=LUoUb4hGMH8 I was looking at the reason as to why a Carnot Engine and watched this video on KhanAcademy. He used a very clever method of proving this by using the ...
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2answers
76 views

Thermodynamic cycles

Consider a system that takes excess air (assume it to be an ideal gas, $Cp = \frac{7}{2} R$) from a power plant stack at $370 \rm K$ (typo in figure) and $2$ bar and compresses it to 20 bar ...