# 4.5 The carnot cycle

 Page 1 / 7
• Describe the Carnot cycle with the roles of all four processes involved
• Outline the Carnot principle and its implications
• Demonstrate the equivalence of the Carnot principle and the second law of thermodynamics

In the early 1820s, Sadi Carnot (1786−1832), a French engineer, became interested in improving the efficiencies of practical heat engines. In 1824, his studies led him to propose a hypothetical working cycle with the highest possible efficiency between the same two reservoirs, known now as the Carnot cycle    . An engine operating in this cycle is called a Carnot engine    . The Carnot cycle is of special importance for a variety of reasons. At a practical level, this cycle represents a reversible model for the steam power plant and the refrigerator or heat pump. Yet, it is also very important theoretically, for it plays a major role in the development of another important statement of the second law of thermodynamics. Finally, because only two reservoirs are involved in its operation, it can be used along with the second law of thermodynamics to define an absolute temperature scale that is truly independent of any substance used for temperature measurement.

With an ideal gas as the working substance, the steps of the Carnot cycle, as represented by [link] , are as follows.

1. Isothermal expansion. The gas is placed in thermal contact with a heat reservoir at a temperature ${T}_{\text{h}}.$ The gas absorbs heat ${Q}_{\text{h}}$ from the heat reservoir and is allowed to expand isothermally, doing work ${W}_{1}.$ Because the internal energy ${E}_{\text{int}}$ of an ideal gas is a function of the temperature only, the change of the internal energy is zero, that is, $\text{Δ}{E}_{\text{int}}=0$ during this isothermal expansion. With the first law of thermodynamics, $\text{Δ}{E}_{\text{int}}=Q-W,$ we find that the heat absorbed by the gas is
${Q}_{\text{h}}={W}_{1}=nR{T}_{\text{h}}\phantom{\rule{0.2em}{0ex}}\text{ln}\frac{{V}_{N}}{{V}_{M}}.$
2. Adiabatic expansion . The gas is thermally isolated and allowed to expand further, doing work ${W}_{2}.$ Because this expansion is adiabatic, the temperature of the gas falls—in this case, from ${T}_{\text{h}\phantom{\rule{0.2em}{0ex}}}\text{to}\phantom{\rule{0.2em}{0ex}}{T}_{\text{c}}.$ From $p{V}^{\gamma }=\phantom{\rule{0.2em}{0ex}}\text{constant}$ and the equation of state for an ideal gas, $pV=nRT$ , we have
$T{V}^{\text{γ}\phantom{\rule{0.2em}{0ex}}\text{−}\phantom{\rule{0.2em}{0ex}}\text{1}}=\text{constant},$

so that
${T}_{\text{h}}{V}_{N}{}^{\gamma -1}={T}_{\text{c}}{V}_{O}{}^{\gamma -1}.$
3. Isothermal compression . The gas is placed in thermal contact with a cold reservoir at temperature ${T}_{\text{c}}$ and compressed isothermally. During this process, work ${W}_{3}$ is done on the gas and it gives up heat ${Q}_{\text{c}}$ to the cold reservoir. The reasoning used in step 1 now yields
${Q}_{\text{c}}=nR{T}_{\text{c}}\phantom{\rule{0.2em}{0ex}}\text{ln}\frac{{V}_{O}}{{V}_{P}},$

where ${Q}_{\text{c}}$ is the heat dumped to the cold reservoir by the gas.
4. Adiabatic compression . The gas is thermally isolated and returned to its initial state by compression. In this process, work ${W}_{4}$ is done on the gas. Because the compression is adiabatic, the temperature of the gas rises—from ${T}_{\text{c}}\phantom{\rule{0.2em}{0ex}}\text{to}\phantom{\rule{0.2em}{0ex}}{T}_{\text{h}}$ in this particular case. The reasoning of step 2 now gives
${T}_{\text{c}}{V}_{P}{}^{\gamma -1}={T}_{\text{h}}{V}_{M}{}^{\gamma -1}.$

The total work done by the gas in the Carnot cycle is given by
$W={W}_{1}+{W}_{2}-{W}_{3}-{W}_{4}.$

what is calorimeter
heat measuring device
Suvransu
What is mean electric potential
Electric density formula
Int E•dA
Vineet
what is relation betweeen potential energy of a system and work done in bringing last chaege from infinity
Einstein and his general theory of relativity, a very nice concept,which revolutionize our modern world.
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
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
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
hello
Nigar
real
Nigar
c'mon guys.. let's talk Physics.
Yoblaze
mass multiplied with latent heat of a substance
Yoblaze
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
it is the product of electric charges and distance between the two charges
Shikhar
mishra true thanks dia
Ssempala
product of separation of the poles, the rest shikhar got is right
brad is separation and distance ,are they different?
Ssempala
What is dielectric
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
What is the difference between specific heat capacity and heat capacity? Give the equations
presentation on power
relation between Celsius and Kelvin
0" degree Celsius=273kelvin
jyotirmayee
Newton's second laws is call with
what is mean by thermodynamics
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
show mathematically that an electron has the greater speed than the proton when they attract each other
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