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.
Hi all,
recently I started following the MIT course "Statistical Mechanics I: Statistical Mechanics Of Particles" by MIT (here).
In the second lesson Prof. Kardar introduces the concept of thermodynamic temperature analyzing the behavior of two Carnot engines that share a thermal reservour at...
***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...
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) ##...
Through an intriguing fictitious dialog between Sadi Carnot and Robert Sterling, Prof. Israel Urieli of the Ohio University shows that it is not required to invoke entropy, the second law of thermodynamics, and the Carnot cycle with the [ideal] adiabatic processes in order to find out the...
I think I calculated part a correctly by extracting the cp (specific heat) of water from the table which is 4.188
Then calculated Q_dot by simply using the equation Q=m*c*deltaT=10.47kW
But I am stuck at part b, I know that the heat extracted from the water is the same as Q_L (rate of heat...
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...
Hey guys! This is problem from Callens Thermodynamics textbook and I'm stuck with it.
My goal was to get a expression for the entropy ##S## which is dependent on ##T## so I can move into the ##T-S##-plane to do my calculations:
I startet by expressing the fundamental equation as a function of...
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...
Let the new engine, NE, extract heat from a certain subset of these baths, and let heat obtained from the ##i^{\rm th}## bath be denoted by ##Q_i##, and let the heat rejected to the ##j^{\rm th}## be denoted by ##Q_j##. Let the engine perform an amount of work ##W##.
Now right beside this...
Is there a mathematical explanation for why the work done in the condenser (in process 2 to 3) is zero? I am aware that ammonia does not expand or compress in the condenser, only changes phase, but without knowing that the process takes place in a condenser and only considering the graph...
If we have that quotient of heats ##Q_2/Q_1=f(t_2,t_1)##, where ##t_1,t_2## are emirical temperatures. Is this function satisfies :
##f(t_2,t_1)=f(t_2-t_1,0)##
I try prove it with Taylor series of two variables, but i can't prove anything.
I know i have to use the efficiency formula and everything is fine but i don't know how to find T its the only unknown in my equation can someone please tell me how to find T . In the solution they got the value of T by equating the work done by the two engines , but why is their work done equal ?
So first I transformed the equation no 2 like this:
$$|Q_L|=K\cdot|W|$$
And then I transformed the first equation to find ##|Q_Z|##
$$|Q_L|=|Q_H|-|W|$$
Plugging the result into the first equation
$$|Q_H|=K\cdot |W|+|W|$$
$$|Q_H|=|W|\cdot (K+1)$$
We know that the efficiency coefficient K is...
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...
I just read about Carnot theorem (the highest efficiency is the one of reversible machines and all reversible machines working between two given temperatures have the same efficiency).
Then I found a problem where I have a reversible cycle made of an isochoric, adiabatic and isotherm. I report...
Hi,
We know that a heat engine working on a Carnot Cycle the efficiency is:
1 - QL/QH = 1 - TL/TH where T is in Kelvin.
But if we use a different absolute temperature scale whose values at TH and TL are different, then the value of efficiency also changes.
I am confused about this issue...
I have my first question. It's about entropy in the Carnot cycle and I'll try to be direct.
The equal sign in the Carnot cycle efficiency equation is related to the fact that the total entropy doesn't change at the end of the whole cycle (being related to the fact that the heat exchanges occur...
Homework Statement
Homework EquationsThe Attempt at a Solution
Trying to figure this out.
So, I'm thinking that adding a extra resevoir for another engine will not add efficiency. It will should split up the W done by the heat reservoir. It just seems to make sense that way. So would the...
Hello
The Carnot cycle has 4 stages.
1. Isothermal relaxation. The gas provides mechanical energy to the piston and receives heat.
2. Adiabatic relaxation. The gas provides mechanical energy to the piston and cools.
3. Isothermal compression. The gas receives mechanical energy from the piston...
"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...
Hi there, I hold an engineering degree and I was just reviewing a page on Wikipedia.
This image specifically demonstrates the impossibility of two theoretical heat engines having different efficiencies between two heat reservoirs. The full Wikipedia page can be found...
Hey guys,
I ran into this paper talking about the Maximum power you can obtain from a Carnot cycle: http://aapt.scitation.org/doi/abs/10.1119/1.10023 From what I understood, there are two extremes. To achieve maximum efficiency you have to make sure that the temperature of the system is never...
In Carnot cycle during the process - "Reversible isothermal heat addition"
Q (supplied) = ∫pdV
This means that the supplied heat is utilized for pdV work.
My doubt is if the Q supplied is converted to work in this process then how Carnot cycle can reject heat during the upcoming isothermal...
A refrigerator operates on a Carnot cycle. In this cycles, it absorbs 120 J of energy at a temperature Tc while 300 J of work is done on the gas undergoing the cycle.
How much energy is exhausted as heat during this process?
The answer is 420 J.
I am unsure of where to start for this...
Given that in a Carnot Cycle the two adiabatic processes are essentially equal and opposite in magnitude the total work done by the cycle is in the two isotherms. The total work of the system is generally given as -NR(Th-Tc)ln(Vb/Va). Does this mean that the work done by a monatomic ideal gas is...
Homework Statement
Carnot theorem states that no engine working between two temperatures T1 of source and T2 of sink can have a greater efficiency than that of the Carnot engine.
Second law of thermodynamics:it is impossible for a self acting machine to transfer heat from a body at a higher...
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...
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...
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...
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...
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...
Hello.
First, look at the figure describing Carnot's cycle.
In 1st step (A → B) and 2nd step (B → C), I fully understand that the work done on the pistol (surrounding) by the gas (system) is dW = pdV where dV = Adl since F = pA is the only force on the pistol from the gas (I assumed there...
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...
Homework Statement
A Carnot engine with water as the working fluid operates with a water recirculation rate of 1 kg/s. For TH = 475 K and TC = 300 K, determine:
a. The pressure of each state
b. The quality of each state
c. The rate of heat addition
d. The rate of heat...
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 –...
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...
Will a rankine cycle have efficiency equal to the carnot cycle, if the mean temperature of heat addition in rankine cycle is equal to the source temperature of Carnot cycle, and the mean temperature of heat rejection is equal to the sink temperature of carnot cycle.
My understanding is that in...
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...
I am learning physics on khan academy and they do a proof to show that delta G for a reversible reaction is negative and how for a irreversible reaction it is positive. However in the proof, they assume that the heat put in by the isotherm is less for an irreversible reaction compared with a...
If a Carnot refrigerator requires a work input of only 230 J to extract 346 J of heat from the cold reservoir.
Doesn’t this discrepancy imply a violation of the law of conservation
of energy?
Homework Statement
Heat engines at negative temperatures. Consider using two heat reservoirs to run an engine (analogous to the Carnot cycle of chapter 3), but specify that both temperatures, T_hot and T_cold, are negative temperatures. The engine is to run reversibly.
(a) If the engine is to...
Homework Statement
A block of radioactive material is ti be used as a power source for a deep space probe which may be treated ideally as a single Carnot engine. Radioactive decay generates heat in the block at a rate Pin = dQin/dt and heat is extracted from the block to operate the probe at a...
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...
Hi Physics Forums,
I'm wondering if a distillation column is limited by the carnot efficiency and, if so, how this limitation can be used to determine the maximum efficiency of a distillation column with particular hot and cold side temperatures.
A distillation column has a hot and cold side...
Hi everyone,
I have been looking at Carnot heat engines in a bid to better understand entropy, and I can't figure out how it actually does work. Why does the piston move?
In some diagrams I have seen weights being removed from the piston, reducing the pressure at constant temperature and...
Homework Statement
I have a question regarding heat engines that cropped up whilst I was doing a practice question. I will summarise the results I obtained for the previous parts of the question so as to save your time. The highlighted parts of the image are where I am having some issues.
I...
Another question, according to catnot efficiency, Qh/Ql=Th/Tl .Can anyone help explain how is this equation derived? It is really frustrating as my textbook doesn't explain this.