<< Chapter < Page Chapter >> Page >
  • 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 h . The gas absorbs heat Q h from the heat reservoir and is allowed to expand isothermally, doing work W 1 . Because the internal energy E int of an ideal gas is a function of the temperature only, the change of the internal energy is zero, that is, Δ E int = 0 during this isothermal expansion. With the first law of thermodynamics, Δ E int = Q W , we find that the heat absorbed by the gas is
    Q h = W 1 = n R T h ln V N V M .
    The figure shows four steps of Carnot cycle, namely isothermal expansion, adiabatic expansion, isothermal compression and adiabatic compression.
    The four processes of the Carnot cycle. The working substance is assumed to be an ideal gas whose thermodynamic path MNOP is represented in [link] .
    The first part of the figure shows a graph corresponding to four steps of Carnot cycle. The x-axis is V and y-axis is p. The second part shows a downward arrow Q subscript h at T subscript h which splits into a downward arrow Q subscript c at T subscript c and a right arrow W.
    The total work done by the gas in the Carnot cycle is shown and given by the area enclosed by the loop MNOPM .
  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 h to T c . From p V γ = constant and the equation of state for an ideal gas, p V = n R T , we have
    T V γ 1 = constant ,

    so that
    T h V N γ 1 = T c V O γ 1 .
  3. Isothermal compression . The gas is placed in thermal contact with a cold reservoir at temperature T c and compressed isothermally. During this process, work W 3 is done on the gas and it gives up heat Q c to the cold reservoir. The reasoning used in step 1 now yields
    Q c = n R T c ln V O V P ,

    where Q 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 c to T h in this particular case. The reasoning of step 2 now gives
    T c V P γ 1 = T h V M γ 1 .

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

Questions & Answers

if 6.0×10^13 electrons are placed on a metal sphere of charge 9.0micro Coulombs, what is the net charge on the sphere
Rita Reply
18.51micro Coulombs
ASHOK
Is it possible to find the magnetic field of a circular loop at the centre by using ampere's law?
Rb Reply
Is it possible to find the magnetic field of a circular loop at it's centre?
Rb Reply
yes
Brother
The density of a gas of relative molecular mass 28 at a certain temperature is 0.90 K kgmcube.The root mean square speed of the gas molecules at that temperature is 602ms.Assuming that the rate of diffusion of a gas in inversely proportional to the square root of its density,calculate the density of
Gifty Reply
A hot liquid at 80degree Celsius is added to 600g of the same liquid originally at 10 degree Celsius. when the mixture reaches 30 degree Celsius, what will be the total mass of the liquid?
Gifty
what is electrostatics
Yakub Reply
Study of charges which are at rest
himanshu
Explain Kinematics
Glory Reply
Two equal positive charges are repelling each other. The force on the charge on the left is 3.0 Newtons. Using your notes on Coulomb's law, and the forces acting on each of the charges, what is the force on the charge on the right?
Nya Reply
Using the same two positive charges, the left positive charge is increased so that its charge is 4 times LARGER than the charge on the right. Using your notes on Coulomb's law and changes to the charge, once the charge is increased, what is the new force of repulsion between the two positive charges?
Nya
A mass 'm' is attached to a spring oscillates every 5 second. If the mass is increased by a 5 kg, the period increases by 3 second. Find its initial mass 'm'
Md Reply
a hot water tank containing 50,000g of water is heated by an electric immersion heater rated at 3kilowatt,240volt, calculate the current
Samuel Reply
what is charge
Aamir Reply
product of current and time
Jaffar
Why always amber gain electrons and fur loose electrons? Why the opposite doesn't happen?
Mohammed Reply
A closely wound search coil has an area of 4cm^2,1000 turns and a resistance of 40ohm. It is connected to a ballistic galvanometer whose resistance is 24 ohm. When coil is rotated from a position parallel to uniform magnetic field to one perpendicular to field,the galvanometer indicates a charge
Palak Reply
Using Kirchhoff's rules, when choosing your loops, can you choose a loop that doesn't have a voltage?
Michael Reply
how was the check your understand 12.7 solved?
Bysteria Reply
Who is ISSAAC NEWTON
LOAK Reply
he's the father of 3 newton law
Hawi
he is Chris Issaac's father :)
Ethem
Practice Key Terms 3

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