Steam Engine Research/Carnot Cycle
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Steam Engine Research
Notes taken from Steam Engineering: A Text Book by William R. King
Overview
The work developed by an engine is not all usefully employed, as there are always loses involved. The ratio of the useful work performed by an engine to the total energy expended is the efficiency of the engine.
A series of operations in physics in which a substance is brought back to its original state is called a cycle. Carnot describes an ideal heat engine consisting of a cylinder and piston of perfect non-conducting material, except for the cylinder head, which is a heat conductor. Three bodies are defined (A, B, and C) which can be applied to the to bottom head of the cylinder:
- A - a source of heat at a constant temperature kept at a temperature, T1.
- B - a non-conductor of heat
- C - a receiver of heat or cooler kept at some temperature T2 (less than T1)
The space between the piston and the bottom of the cylinder is defined to contain a working substance which is a perfect gas of temperature T1.
The cycle has four operations as follows:
1. Apply the hot body A to the bottom head of the cylinder. The gas in the cylinder expands causing the piston to move and do work. The pressure in the cylinder falls, but the gases receives sufficient heat from A to maintain its temperature at T1. This is an isothermal expansion represented by ab in Fig. 137. When it has reached the point b, the first operation is complete.
2. Remove A and apply the non-conductor B. The piston continues to move because of the internal energy of the gas acting on it. The temperature falls to T1. This completes the second operation.
3. Remove B and apply C thus cooling the gas in the cylinder and forcing the piston back, compressing the gas in the process. The slight increase in temperature of the temperature of the gas is due to compression and causes sufficient heat to pass the gas from the cooler C to maintain the temperature of the gas at T2. When the compression has proceeded to d in Fig. 137, the third operation cd is complete. Since the temperature of the gas was maintained at T2, the compression is isothermal.
4. Remove C and apply B, continuing the compression. The temperature and pressure of the gas continues to rise. If the point d is properly chosen, the gas will have compressed to its original pressure and will have arrived again at temperature T1 when the piston returns to its original position. The point d must be chosen such that an adiabatic curve through d will pass through a. This last operation completes the cycle.
In the above cycle, the three bodies were applied in the order of A-B-C-B. If the order is changed to B-C-B-A, the diagram in Fig. 137 will be traced in the opposite direction, with exactly the reverse of heat transfers at temperatures T1 and T2. This describes a reversible or perfect heat engine.
Calculations
