<< Chapter < Page Chapter >> Page >
The photo shows gases releasing from a power plant.
The heat exhausted from a nuclear power plant goes to the cooling towers, where it is released into the atmosphere.

Heat engines operate by carrying a working substance through a cycle. In a steam power plant, the working substance is water, which starts as a liquid, becomes vaporized, is then used to drive a turbine, and is finally condensed back into the liquid state. As is the case for all working substances in cyclic processes, once the water returns to its initial state, it repeats the same sequence.

For now, we assume that the cycles of heat engines are reversible, so there is no energy loss to friction or other irreversible effects. Suppose that the engine of [link] goes through one complete cycle and that Q h , Q c , and W represent the heats exchanged and the work done for that cycle. Since the initial and final states of the system are the same, Δ E int = 0 for the cycle. We therefore have from the first law of thermodynamics,

W = Q Δ E int = ( Q h Q c ) 0 ,

so that

W = Q h Q c .

The most important measure of a heat engine is its efficiency ( e )    , which is simply “what we get out” divided by “what we put in” during each cycle, as defined by e = W out / Q in .

With a heat engine working between two heat reservoirs, we get out W and put in Q h , so the efficiency of the engine is

e = W Q h = 1 Q c Q h .

Here, we used [link] , W = Q h Q c , in the final step of this expression for the efficiency.

A lawn mower

A lawn mower is rated to have an efficiency of 25.0 % and an average power of 3.00 kW. What are (a) the average work and (b) the minimum heat discharge into the air by the lawn mower in one minute of use?

Strategy

From the average power—that is, the rate of work production—we can figure out the work done in the given elapsed time. Then, from the efficiency given, we can figure out the minimum heat discharge Q c = Q h ( 1 e ) with Q h = Q c + W .

Solution

  1. The average work delivered by the lawn mower is
    W = P Δ t = 3.00 × 10 3 × 60 × 1.00 J = 180 kJ .
  2. The minimum heat discharged into the air is given by
    Q c = Q h ( 1 e ) = ( Q c + W ) ( 1 e ) ,

    which leads to
    Q c = W ( 1 / e 1 ) = 180 × ( 1 / 0.25 1 ) kJ = 540 kJ .

Significance

As the efficiency rises, the minimum heat discharged falls. This helps our environment and atmosphere by not having as much waste heat expelled.

Got questions? Get instant answers now!

Summary

  • The work done by a heat engine is the difference between the heat absorbed from the hot reservoir and the heat discharged to the cold reservoir, that is, W = Q h Q c .
  • The ratio of the work done by the engine and the heat absorbed from the hot reservoir provides the efficiency of the engine, that is, e = W / Q h = 1 Q c / Q h .

Conceptual questions

Explain in practical terms why efficiency is defined as W / Q h .

Got questions? Get instant answers now!

Problems

An engine is found to have an efficiency of 0.40. If it does 200 J of work per cycle, what are the corresponding quantities of heat absorbed and rejected?

Got questions? Get instant answers now!

In performing 100.0 J of work, an engine rejects 50.0 J of heat. What is the efficiency of the engine?

0.667

Got questions? Get instant answers now!

An engine with an efficiency of 0.30 absorbs 500 J of heat per cycle. (a) How much work does it perform per cycle? (b) How much heat does it reject per cycle?

Got questions? Get instant answers now!

It is found that an engine rejects 100.0 J while absorbing 125.0 J each cycle of operation. (a) What is the efficiency of the engine? (b) How much work does it perform per cycle?

a. 0.556; b. 125.0 J

Got questions? Get instant answers now!

The temperature of the cold reservoir of the engine is 300 K. It has an efficiency of 0.30 and absorbs 500 J of heat per cycle. (a) How much work does it perform per cycle? (b) How much heat does it reject per cycle?

Got questions? Get instant answers now!

The Kelvin temperature of the hot reservoir of an engine is twice that of the cold reservoir, and work done by the engine per cycle is 50 J. Calculate (a) the efficiency of the engine, (b) the heat absorbed per cycle, and (c) the heat rejected per cycle.

a. 0.50; b. 100 J; c. 50 J

Got questions? Get instant answers now!

A coal power plant consumes 100,000 kg of coal per hour and produces 500 MW of power. If the heat of combustion of coal is 30 MJ/kg, what is the efficiency of the power plant?

Got questions? Get instant answers now!

Questions & Answers

what is calorimeter
odionyenma Reply
heat measuring device
Suvransu
What is mean electric potential
Biren Reply
Electric density formula
Biren Reply
Int E•dA
Vineet
what is relation betweeen potential energy of a system and work done in bringing last chaege from infinity
Shikhar Reply
Einstein and his general theory of relativity, a very nice concept,which revolutionize our modern world.
Antares Reply
what's the theory of relativity?
Piyali
it related to universe time period
jyotirmayee
it is a theory in which time is taken as relative,for diff. motion of objects.
Antares
no !!!
jyotirmayee
it is E=mc'square
jyotirmayee
what is black hole?
jyotirmayee
E=mc^2 is just a reln which sums up everything dude
Antares
what does e=mc^2 stand for?explain
Piyali
m not dude
jyotirmayee
e for speed of light
jyotirmayee
c for speed of light
jyotirmayee
m for mass of object
jyotirmayee
black hole is a super massive object in space gravitation pull of which s so strong dt evn light cannot escape. John wheeler 1st detected it, n concept of it ws given by Einstein himself from his general theory of relativity. Basically v cn si 3 types of it super massive, interstellar n intermediate
Antares
which topic now u studying?
jyotirmayee
e defined? sorry it,s wrong
jyotirmayee
Why?
Arzoodan
how black holes r formed?
Piyali
e is not speed of light
jyotirmayee
black holes formed when the centre of very massive star collapsed itself
jyotirmayee
e is energy.
Antares
what do u mean by quantum mechanics?
jyotirmayee
in most of d cases black holes r formed by massive collapsed star or star system
Antares
sahoo u don't seem to understand relative physics, plz study that first.
Antares
exatly...
Arzoodan
Apollo is the name of a satellite !!!!!
jyotirmayee
quantum mechanics is d study of physics describing nature at d smallest level of energy of atoms n subatomic particles.
Antares
qm means explains about the microscopic particles..
KRANTHI
nope name of d sun god
Antares
why the mercury used in thermometers?
jyotirmayee
Ali brother ur exactly spelling is wrong,,,,,
jyotirmayee
why the colour of tube light white?
jyotirmayee
why the mouth became red colour ,,by the regular eating of leaf called ,,betel combining with areca?
jyotirmayee
all formula for calculate specific latent heat of any substance
Idowu Reply
hello
Nigar
Hi, your real Nigga...? Or this jock?
Arzoodan
real
Nigar
You from Pakistan or India?
Arzoodan
c'mon guys.. let's talk Physics.
Yoblaze
mass multiplied with latent heat of a substance
Yoblaze
What you doing about Physics
Arzoodan
you both?
jyotirmayee
in which class?
jyotirmayee
physics is the only subject which underestimated chemistry ,,bio
jyotirmayee
how capacitor is made in inst?
Piyali
what is dipole moment
Bilal Reply
it is the product of electric charges and distance between the two charges
Shikhar
yeap. this correct answer...
Arzoodan
mishra true thanks dia
Ssempala
product of separation of the poles, the rest shikhar got is right
Brad
brad is separation and distance ,are they different?
Ssempala
What is dielectric
Ashis Reply
its a type of medium. generally poor conductors. but their conductivity can be changed
vedanth
you just have to add impurities
vedanth
Thanks
Ssempala
grt
Ssempala
a material which behave as conductor
Shikhar
insulating material, energy level for electron transfer is very high e.g used to increase a magnetic field in a capacitor
Brad
What is the difference between specific heat capacity and heat capacity? Give the equations
elly Reply
presentation on power
Dyutee Reply
relation between Celsius and Kelvin
Anish Reply
0" degree Celsius=273kelvin
jyotirmayee
Newton's second laws is call with
Dyutee Reply
what is mean by thermodynamics
Prasad Reply
it is study about temperature and it's equilibrium
thiru
Its the study of heat and its relation with others kind of energy
Antonio
state caulombs law clearly
constand Reply
show mathematically that an electron has the greater speed than the proton when they attract each other
ezra Reply
show mathematically that an electron has the greater speed than the proton when they attract each other
srikanta
@ezra & srikanta; for electrons: a=ke^2/(mr^2) and for protons: a=kp^2/(mr^2)
Sikandar
Practice Key Terms 4

Get the best University physics vol... course in your pocket!





Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'University physics volume 2' conversation and receive update notifications?

Ask