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Computer drawing of a p-V plot of the Carnot Cycle.

Thermodynamics is a branch of physics which deals with the energy and work of a system. Thermodynamics deals with the large scale response of a system which we can observe and measure in experiments. As aerodynamicists, we are most interested in the thermodynamics of propulsion systems and high speed flows. To understand how a propulsion system works, we must study the basic thermodynamics of gases.

Gases have various properties that we can observe with our senses, including the gas pressure p, temperature T, mass, and volume V that contains the gas. Careful, scientific observation has determined that these variables are related to one another, and the values of these properties determine the state of the gas. A thermodynamic process, such as heating or compressing the gas, changes the values of the state variables in a manner which is described by the laws of thermodynamics. The work done by a gas and the heat transferred to a gas depend on the beginning and ending states of the gas and on the process used to change the state.

It is possible to perform a series of processes, in which the state is changed during each process, but the gas eventually returns to its original state. Such a series of processes is called a cycle and forms the basis for understanding engines. The Carnot Cycle is one of the fundamental thermodynamic cycles and is described on this web page. We will use a p-V diagram to plot the various processes in the Carnot Cycle. The cycle begins with a gas, colored yellow on the figure, which is confined in a cylinder, colored blue. The volume of the cylinder is changed by a moving red piston, and the pressure is changed by placing weights on the piston. We have two heat sources; the red one is at a nominal 300 degrees, and the purple one is at 200 degrees. Initially, the gas is in State 1 at high temperature, high pressure, and low volume.

  • The first process performed on the gas is an isothermal expansion. The 300 degree heat source is brought into contact with the cylinder, and weight is removed, which lowers the pressure in the gas. The temperature remains constant, but the volume increases. During the process from State 1 to State 2 heat is transferred from the source to the gas to maintain the temperature. We will note the heat transfer by Q1 into the gas.
  • The second process performed on the gas is an adiabatic expansion. During an adiabatic process no heat is transferred to the gas. Weight is removed, which lowers the pressure in the gas. The temperature decreases and the volume increases as the gas expands to fill the volume. During the process from State 2 to State 3 no heat is transferred.
  • The third process performed on the gas is an isothermal compression. The 200 degree heat source is brought into contact with the cylinder, and weight is added, which raises the pressure in the gas. The temperature remains constant, but the volume decreases. During the process from State 3 to State 4 heat is transferred from the gas to heat source to maintain the temperature. We will note the heat transfer by Q2 away from the gas.
  • The fourth process performed on the gas is an adiabatic compression. Weight is added, which raises the pressure in the gas. The temperature increases and the volume decreases as the gas is compressed. During the process from State 4 to State 1 no heat is transferred.

At the end of the fourth process, the state of the gas has returned to its original state and the cycle can be repeated as often as you wish. During the cycle, work W has been produced by the gas, and the amount of work is equal to the area enclosed by the process curves. From the first law of thermodynamics, the amount of work produced is equal to the net heat transferred during the process:

W = Q1 - Q2

The Carnot Cycle has performed as an engine, converting the heat transferred to the gas during the processes into useful work. A similar Brayton Cycle explains how a gas turbine engine works, and an Otto Cycle explains how an internal combustion engine works.



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Editor: Tom Benson
NASA Official: Tom Benson
Last Updated: Jun 12 2014

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