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Since temperatures are given for the hot and cold reservoirs of this heat engine, Eff C = 1 T c T h size 12{ ital "Eff" rSub { size 8{C} } =1- { {T rSub { size 8{c} } } over {T rSub { size 8{h} } } } } {} can be used to calculate the Carnot (maximum theoretical) efficiency. Those temperatures must first be converted to kelvins.


The hot and cold reservoir temperatures are given as 300 º C size 12{"300"°C} {} and 27 . 0 º C size 12{"27" "." 0°C} {} , respectively. In kelvins, then, T h = 573 K and T c = 300 K size 12{T rSub { size 8{c} } ="300"" K"} {} , so that the maximum efficiency is

Eff C = 1 T c T h . size 12{ ital "Eff" rSub { size 8{C} } =1 - { {T rSub { size 8{c} } } over {T rSub { size 8{h} } } } } {}


Eff C = 1 300 K 573 K = 0 . 476 , or  47 . 6% . alignl { stack { size 12{ ital "Eff" rSub { size 8{C} } =1- { {"300"" K"} over {"573"" K"} } } {} #=0 "." "476"", or ""47" "." 6% "." {} } } {}


A typical nuclear power station’s actual efficiency is about 35%, a little better than 0.7 times the maximum possible value, a tribute to superior engineering. Electrical power stations fired by coal, oil, and natural gas have greater actual efficiencies (about 42%), because their boilers can reach higher temperatures and pressures. The cold reservoir temperature in any of these power stations is limited by the local environment. [link] shows (a) the exterior of a nuclear power station and (b) the exterior of a coal-fired power station. Both have cooling towers into which water from the condenser enters the tower near the top and is sprayed downward, cooled by evaporation.

Part a shows a photograph of an operational nuclear power plant in night view. There are dome shaped structures which house radioactive material and vapors are shown to come from two cooling towers. Part b shows a photograph of a coal fired power plant. Several huge cooling towers are shown.
(a) A nuclear power station (credit: BlatantWorld.com) and (b) a coal-fired power station. Both have cooling towers in which water evaporates into the environment, representing Q c size 12{Q rSub { size 8{c} } } {} . The nuclear reactor, which supplies Q h size 12{Q rSub { size 8{h} } } {} , is housed inside the dome-shaped containment buildings. (credit: Robert&Mihaela Vicol, publicphoto.org)

Since all real processes are irreversible, the actual efficiency of a heat engine can never be as great as that of a Carnot engine, as illustrated in [link] (a). Even with the best heat engine possible, there are always dissipative processes in peripheral equipment, such as electrical transformers or car transmissions. These further reduce the overall efficiency by converting some of the engine’s work output back into heat transfer, as shown in [link] (b).

Part a of the diagram shows a combustion engine represented as a circle to compare the efficiency of real and Carnot engines. The hot reservoir is a rectangular section above the circle shown at temperature T sub h. A cold reservoir is shown as a rectangular section below the circle at temperature T sub c. Heat Q sub h enters the heat engine as shown by a bold arrow. For a real engine a small part of it is shown to be expelled as output from the engine shown as a bold arrow leaving the circle and for a Carnot engine larger part of it is shown to leave as work shown by a dashed arrow leaving the circle. The remaining heat is shown to be returned back to the cold reservoir as shown by bold arrow toward it for real engines and comparatively lesser heat is given by the Carnot engine shown by a dashed arrow. Part b of the diagram shows an internal combustion engine represented as a circle to study friction and other dissipative processes in the output mechanisms of a heat engine. The hot reservoir is a rectangular section above the circle shown at temperature T sub h. A cold reservoir is shown as a rectangular section below the circle at temperature T sub c. Heat Q sub h enters the heat engine as shown by a bold arrow, work W is produced as output, shown leaving the system, and the remaining heat Q sub c and Q sub f are returned back to the cold reservoir as shown by bold arrows toward it. Q sub f is heat due to friction. The work done against friction goes as heat Q sub f to the cold reservoir.
Real heat engines are less efficient than Carnot engines. (a) Real engines use irreversible processes, reducing the heat transfer to work. Solid lines represent the actual process; the dashed lines are what a Carnot engine would do between the same two reservoirs. (b) Friction and other dissipative processes in the output mechanisms of a heat engine convert some of its work output into heat transfer to the environment.

Section summary

  • The Carnot cycle is a theoretical cycle that is the most efficient cyclical process possible. Any engine using the Carnot cycle, which uses only reversible processes (adiabatic and isothermal), is known as a Carnot engine.
  • Any engine that uses the Carnot cycle enjoys the maximum theoretical efficiency.
  • While Carnot engines are ideal engines, in reality, no engine achieves Carnot’s theoretical maximum efficiency, since dissipative processes, such as friction, play a role. Carnot cycles without heat loss may be possible at absolute zero, but this has never been seen in nature.

Conceptual questions

Think about the drinking bird at the beginning of this section ( [link] ). Although the bird enjoys the theoretical maximum efficiency possible, if left to its own devices over time, the bird will cease “drinking.” What are some of the dissipative processes that might cause the bird’s motion to cease?

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Questions & Answers

a thick glass cup cracks when hot liquid is poured into it suddenly
Aiyelabegan Reply
because of the sudden contraction that takes place.
railway crack has gap between the end of each length because?
Aiyelabegan Reply
For expansion
Please i really find it dificult solving equations on physic, can anyone help me out?
Big Reply
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fersnels biprism spectrometer how to determined
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how to study the hall effect to calculate the hall effect coefficient of the given semiconductor have to calculate the carrier density by carrier mobility.
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Nana Reply
find the dimensional equation of work,power,and moment of a force show work?
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Michelson Morley experiment
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Calculate the final velocity attained, when a ball is given a velocity of 2.5m/s, acceleration of 0.67m/s² and reaches its point in 10s. Good luck!!!
Eklu Reply
vf=vi+at vf=2.5+ 0.67*10 vf= 2.5 + 6.7 vf = 9.2
s = vi t +1/2at sq s=58.5 s=v av X t vf= 9.2
how 2.68
v=u+at where v=final velocity u=initial velocity a=acceleration t=time
the answer is 9.2m/s
express your height in Cm
Emmanuel Reply
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Emmanuel Reply
Two bodies P and Quarter each of mass 1000g. Moved in the same direction with speed of 10m/s and 20m/s respectively. Calculate the impulse of P and Q obeying newton's 3rd law of motion
Shimolla Reply
the answer is 0.03n according to the 3rd law of motion if the are in same direction meaning they interact each other.
definition for wave?
Doc Reply
A disturbance that travel from one medium to another and without causing permanent change to its displacement
In physics, a wave is a disturbance that transfers energy through matter or space, with little or no associated mass transport (Mass transfer). ... There are two main types ofwaves: mechanical and electromagnetic. Mechanicalwaves propagate through a physical matter, whose substance is being deformed
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Note: LINEAR MOMENTUM Linear momentum is defined as the product of a system’s mass multiplied by its velocity: size 12{p=mv} {}
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Study of matter and energy
physics is the science of matter and energy and their interactions
physics is the technology behind air and matter
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31. Calculate the initial (from rest) acceleration of a proton in a 5.00×106 N/C electric field (such as created by a research Van de Graaff). Explicitly show how you follow the steps in the Problem-Solving Strategy for electrostatics.
Catina Reply
A tennis ball is projected at an angle and attains a range of 78. if the velocity is 30metres per second, calculate the angle
what friction
Wisdom Reply
question on friction
the rubbing of one object or surface against another.
momentum is the product of mass and it's velocity.
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Friction is a force that exist between two objects in contact. e.g. friction between road and car tires.
Practice Key Terms 3

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