GITAM, Department of Engineering Physics


 

Main discoveries of Sadi Carnot that led to the foundation of thermodynamics


         Carnot Cycle

The Carnot cycle is the most efficient cycle possible. It consists of four basic reversible processes meaning that the cycle as a whole is also reversible. The four reversible processes are:

1. Isothermal expansion (by placing the system in contact with a heat reservoir with temperature T1).

2. Adiabatic expansion to T2 < T1.

3. Isothermal compression (by placing the system in contact with a heat reservoir with temperature T2).

4. Adiabatic compression from T2 to T1.

         Carnot Engine

Engine using a Carnot cycle of operations. This type of engine can serve as the model for a thermic or refrigerator engine. An "animation" facilitates a better understanding of the cycle :

1.                       Air at temperature T1 is held in a cyclinder, closed by an insulated piston (starting position: cd). A hot source A, with temperature T1, and a cold source B, with temperature T2, constitute infinite reservoirs of heat.

2.                       The cylinder is put in contact with A: the heat passes from the source to the air, that relaxes freely and pushes the piston to the position ef.

3.                       The cylinder is isolated from all source of heat. During its adiabatic expansion, the air pushes the piston until gh: its temperature falls to T2.

4.                       The cylinder, with temperature T2 then, is put in contact with the heat source B, with identical temperature. A "theoretical" experimenter pushes the piston downwards: this isothermal compression brings it to position cd. Heat passes from the air to the source B.

5.                       The cylinder is isolated from the outside again. The "theoretical" experimenter continues to push the piston until it reaches position ik, in such a way that the air temperature reaches T1.

6.                       The cylinder is put in contact with A, which delivers heat to the air: it expands until the piston comes back to its initial position cd.

         Carnot's Principle

An irreversible heat engine operating between two heat reservoirs at constant temperatures cannot have an efficiency greater than that of a reversible heat engine operating between the same two temperatures.

Another form of the Second Law of Thermodynamics or Carnot's Principle is that : It is not possible to make a heat engine whose only effect is to absorb heat from a high-temperature region and turn all that heat into work. That is, it is not possible to design a heat engine that does not exhaust heat to the environment. Or, it is not possible to design a heat engine that has an efficiency of 1.00 or 100%.

         Carnot's Theorem

During one part of the cycle performed in an engine, some heat is absorbed from a hot reservoir. During another part, a smaller amount of heat is rejected to a cooler reservoir. The engine is therefore said to operate between these two reservoirs. It is a fact of experience that some heat is always rejected to the cooler reservoir. Because of this, the efficiency of an actual engine is never 100%. The first cycle we will look at is the Carnot cycle.The processes that make up this cycle are either isothermal or adiabatic.

For an ideal gas Carnot cycle, the four steps are shown below:

  1. Isothermal expansion from Va,Pa to Vb,Pb at Thot absorbing heat Qh.
  2. Reversible adiabatic expansion from Vb,Pb to Vc,Pc as the temperature falls from Thot to Tcold.
  3. Isothermal contraction from Vc,Pc to Vd, Pd at Tcold exhausting heat Qc.
  4. Reversible adiabatic contraction from Vd,Pd to Va,Pa as the temperature rises from Tcold to Thot.

 

The system has returned to its initial state and an amount of work, W, has been done to the system. By the conservation of energy,

                                                                                        Equation (1).

The PV diagram for this cycle is shown in Figure (1) below.

 

The thermal efficiency, n, of a cycle operating as a heat engine is defined as

                                                                                                    Equation (2).

The absolute value sign was used to eliminate any confusion about which way the heat is flowing and whether Q is positive or negative. We can use conservation of energy in the form of Equation (1) to find the efficiency of the cycle in terms of the Qc and Qh.

                                                                                                    Equation (3).

Equations (2) and (3) apply to any cycle. The Carnot cycle is useful in studying real engines and refrigerators largely because one can derive the efficiency of the ideal gas Carnot cycle in terms of the temperatures of the heat reservoirs.