Questions tagged [carnot-cycle]

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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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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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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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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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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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40 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
70 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
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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
78 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
107 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
281 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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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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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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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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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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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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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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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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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
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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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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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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
88 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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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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162 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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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
110 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
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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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2answers
165 views

Calculating efficiency of a Engine

Given are four points in a PV-diagram: $(V_1, 3/2P_1)$ is the leftmost point, $(V_2,3/2P_1)$ is the rightmost point, $(\frac{V_1+V_2}{2},P_1)$ is the lowest point and $(\frac{V_1+V_2}{2},2P_1)$ is the ...
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321 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
224 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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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
321 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
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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
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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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561 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
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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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228 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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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
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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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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 ...
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Does chaining Carnot heat engines make them more efficient?

Since the efficiency of a Carnot cycle depends on the difference between the hot and cold sides of the engine, could you put multiple heat engines in a series to maximize overall efficiency? A $3000 \,...
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Total Reversibility of Carnot Cycle

I was reading about Carnot cycle in "Thermodynamics by Cengel & Boles", now it is stated that Carnot cycle is a totally reversible cycle, i.e it is an internally as well as externally reversible ...
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Could a Carnot engine linked to a Carnot “refrigerator” create a perpetual heat flow between two reservoirs?

Here is a diagram of the system in question (adapted from the diagram on this page): All of the work produced by the Carnot engine is used to drive the Carnot refrigerator, which is simply a Carnot ...
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267 views

Actual sequence of refrigeration cycle

Whenever i have studied refrigeration cycle on books, i have found that the diagrams are always explained starting from the compressor*, then condenser then throttle and finally evaporator. I find it ...
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441 views

Validity of Carnot's theorem when operating between finite reservoirs

Carnot’s theorem tells us that "the most efficient heat engines operating between 2 reservoirs have the same efficiency as a Carnot engine". This theorem assumes that the engines are operating ...
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1answer
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Reversible and irreversible cycles: Changes in entropy of the system and the surrounding

Entropy is a state function. Is it true that at the end of a cyclic process, the change in entropy of the of the system and that of its surrounding are both separately zero irrespective of whether ...
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3answers
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Is there an implemented example of an almost reversible heat engine?

I'm reading Feynman's discussion of Reversible engines (Vol I 44.3) in The Feynman Lectures on Physics. His discussion is very abstract, and leaves a lot of practical questions unanswered. Rather ...
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Heat transfer in the isothermal expansion in the Carnot cycle

Problem In the Carnot cycle there are two adiabatic and two isothermal processes. This question focuses on the isothermal expansion. In the isothermal expansion books often writes that the system is ...