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.
Homework Statement
A Carnot heat 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. In 5 minutes of operation of the engine, the heat rejected by the engine melts a mass of ice equal to 3.30×10^-2 kg...
1.
Homework Statement
1) A 200 litre container of boiling water and a 200 litre of ice cold water are used as heat source and sink for a carnot engine. Calculate the maximum amount of useful work that can be obtained from the system and the final temperature of the two containers of water...
Homework Statement
An ice-making machine inside a refrigerator operates in a Carnot cycle. It takes heat from liquid water at 0.0C and rejects heat to a room at a temperature of 25.0C. Suppose that liquid water with a mass of 78.3kg at 0.0C is converted to ice at the same temperature...
Homework Statement
We have stressed that the Carnot engine does not exist in real life: It is a purely theoretical device, useful for understanding the limitations of heat engines. Real engines never operate on the Carnot cycle; their efficiency is hence lower than that of the Carnot engine...
Is it possible to show that the maximum efficiency for a heat engine is given by
\eta = 1 - \frac{T_c}{T_h}
where T_c is the temperature of the cold sink and T_c is the temperature of the warm sink?
In other words: How do I prove that a engine run by a Carnot cycle is the most efficient engine?
i have this example problem...and i want to know how to answer this problem :confused:
a carnot engine is operated with its maximum temperature equal to 700K and 300kW were rejected. what is the sink temperature, if 450kW enters at the upper temperature.
tanx for your help..
hi i just want to know the formula of the otto cycle for the folowwing parameter:
compression ratio,cycle work,heat added,heat rejection,thermal efficiency and mean effective pressure.
and also may i know the formula for getting the pressure (bar) and the volume(m3/kg) temperature(K) for...
Hi,
I need some help concerning the Carnot cycle [i've searched, but what i needed didn't come up]. I am trying to work out the efficiency of a 4 or 2 stroke motorcyle engine. [car engine, it doesn't matter really]. But I'm having some difficulty finding temperatures for the hot and cold...
Homework Statement
There are two Carnot engines in series, so that the heat exhaust from the first engine drives the second. Find the overall efficiency of the arrangement which contains only the efficiences of the individual engines.
Homework Equations
\epsilon = \frac{W}{Q_{input}}...
The inside of an ideal refrigerator is at a temperature , while the heating coils on the back of the refrigerator are at a temperature . Owing to a malfunctioning switch, the light bulb within the refrigerator remains on when the the door is closed. The power of the light bulb is ; assume that...
Homework Statement
Under many conditions, the rate at which heat enters as air conditioned building on a hot summer day is proportional to the difference in the temperature between the inside and outside, Th-Tc. (If the heat enters entirley by conduction,this statement will certainly be...
Homework Statement
Specify that the finite reservoirs of a Carnot cycle start at initial temperatures T_h and T_c. Acknowledge the consequence of the finiteness of the reservoirs: the hot reservoir will drop in temperature and the cold reservoir will increase in temperature. The two...
Halliday says that the efficiency of an ideal Stirling engine is lower than that of a ideal Carnot engine?? But why??
It seems to me that there efficiency are both \epsilon =1-\frac{T_L}{T_H}
Though Halldiay also say that this equation do not apply to Stirning engine but only to Carnot...
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 5650 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...
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 6600 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 the heat delivered...
Homework Statement
a) Assume that a Carnot cycle is used to achieve that 250kg of water at 0 degrees celsius is frozen into ice using an ideal refigerator The room temperature is 27 degrees. What is the minimum amount of work input to the refrigerator to achieve this?
b)Assume the refigerator...
A Carnot refrigerator operating between -10.0 C and 40.0 C extracts heat from the cold reservoir at the rate 300 J/s. What are (a) the coefficient of performance of this refrigerator, (b) the rate at which work is done on the refrigerator and (c) the rate at which heat is exhausted to the hot...
Consider a Carnot engine operating between temperatures T_h_ and T_c_, where T_c_ is above the ambient temperature T_o_. A second engine operates between the temperatures T_c_ and T_o_.
Calculate (in terms of temperatures) the overall efficiency of the two-stage engine operating this way, and...
My book states:
"To prove that no real heat engine operating between two reservoirs is more efficient than a carnot engine between the same reservoirs, imagine a more efficient engine to drive a less efficient carnot refrigerator. For the combination of the engine and refrigerator you get a...
Hello to all,
this is my first post on this forum. I'm electrical engineer (technical informatics) but in my spare time I'm interested in thermodynamics especially about steam cycle in power plant.
I know that condenser is meant to convert steam to water and here we have pure losses of...
Is there a formula used to solve engine problems? For example a carnot engine is operated between two heat reservoirs at temperatures of 500K and 300K. If the engine receives 200 cal from the reservoir at 500K in each cycle. How many calories does it reject to the reservior at 300K?
This...
Suppose you had the choice of either raising the high-temperature reservoir a certain number of kelvins, or lowering the low-temperature reservoir the same number of kelvins. Which would you choose (assuming you wanted to increase the efficiency, of course)?
After doing experimenting with...
Calculate the ideal (Carnot) efficiency of a heat engine operating between 23.0 degrees and 515 degrees. How much heat would be rejected by the engine if 1.00 x 10^6 calories were taken from the high temperature resivoir.
Would you just use e=1-(T(c)/T(H))?
And for the second part i don't...
I have a question regarding Carnot Cycles and Adiabatic processs.
I have cylinder with n moles of a mono-atomic gas with a specific Volume, Pressure and Temperature. This Cylinder is closed by a piston.
This system undergoes the four step Carnot Cycle A-B, B-C, C-D and D-A.
A-B: Is...
a firebox is at 750K and the ambient temp is 300K. The efficiency of a Carnot engine doing 150J of work as it transports energy between these constant temperature baths is 60%. The Carnot engine must take in energy 150/.60=250J from the hot reservoir and must put out 100J of energy by heat...
integration of
Dear people of this section.
Suppose you have two indepenfent functions x and y and we need to find the integral of the following expression y dx ,and y does not depends upon x, but y varies between 4 and 8 in the interval of integration. ¿ Do you think that the value of the...
Problem :
Consider an engine in outer space which operates on the Carnot cycle. The only way in which heat can be transferred from the engine is by radiation. The rate at which heat is radiated is proportional to the fourth power of the absolute temperature and the area of the radiating...
Dear people of Physics Forums, I would like to have your opinion about the following problem: Suppose we are interested to evaluate the average efficiency ( e ) of an infinite series of carnot cycles. The temperature of the hot reservoir of each carnot Cycle of the series, Ta, is at 990K, but...
hey everyone,
I need some help solving the following problem. I am kind of confused on where to start. here is the question from the book.
A carnot refrigerator is operated between two heat reservoirs at temperatures of 320K and 270K.
a) If in each cycle the refrigerator receives 415J...
The question reads...
A heat pump is essentially a refrigerator engine that uses the inside of a building as a hot reservoir in the winter and the outside of the building as the hot reservoir in the summer. A) For a carnot refrigerator engine operating between 25 C and 40 C in the summer, what...
In class, we're being introduced to thermodynamics, and one of the topics is heat engines.
Steam engines were also mentioned.
Carot engines also entered the pic. They are described as ideal systems. Exactly why are Carnot engines not "real" engines, or are not possible?
I'm sorry if...
Hi there,
I have what should be a simple problem, but it's driving me insane.
Here's the problem: A Carnot air conditioner maintains the temperature in a house at 290 K on a day when the temperature outside is 315 K. What is the coefficient of performance of the air conditioner?
So I...
Pls who can help me with this following problem?
A real heat engine operates between temperatures Tc and Th. During a certain time, an amount Qc of heat is released to the cold reservoir. During that time, what is the maximum amount of work that the engine might have performed?
Thank you
This is just a common problem solving question, which I cannot make, I suspect because I'm bad at maths. Anyway, I want to see it done, hopefully to grasp it. I am doing physics, so, it's an exercise from one of my books.
18-11. Show that the efficiency e of a Carnot engine and the...
Hey everyone,
I was sick when we started this unit. I've been trying to catch up, and need to ask a couple of broad questions.
1) What is a Carnot engine? Or the Carnot cycle? What is it used for ? Why do we can about perfect conditions??
2) When people keep mentioning...
I'm not sure I understand why the Carnot cycle involves adiabatic processes at all. I can't seem to find a reason. Also on a related note, how exactly does a Carnot heat pump (refrigerator type) work? Is the sequence the same as a Carnot heat engine?
Hi, I would appreciate any help with this:
A monatomic ideal gas is used as the working substance for
the Carnot cycle. Processes A => B and C => D
are isothermal, while processes B => C and D => A are adiabatic.
During process A => B, there are 400 J of work done by the gas on
the...
I have to corellate the Carnot cycle with line integrals. This makes sense to me as line integrals can be used to find the work done by a vector field on an object traveling along a certain path. The Carnot cycle places a limit on the efficiency of an engine cycle.
My question, how could I...