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The Carnot Cycle
The Carnot Cycle== The graph showing pressure against volume can be used to determine the work done by a gas by looking at the area enclosed by the cycle. This results from potential energy changed by the altering bonding of the gas.
Heat engines such as internal combustion engines operate in a cycle, adding heat in one part of the cycle and using some of the heat to do useful work in another part of the cycle. The Carnot cycle represents the most thermally efficeint sequence of changes that xan convert a certain amount of heat into useful work.
Carnot chose an ideal gas to be the working substance in his ideal heat engine. The engine would operate between a hot reservoir at the temperature Th and a cold reservoir at temperature Tc. The paths on the pressure volume graph are reversible so heat can be extracted or supplied or work done to the system at any time to cause it to reverse. The Carnot cycle is composed of two isothermal paths in which the temperature is constant and two abdiatic paths where no heat enters or leaves the system.
From A-B (on the graph): The gas expands and does work on it's surroundings while the engine absorbs heat from a source (the hot reservoir). Along this isothermal, the internal energy and temperature of the gas does not change.
-W=Q
From B-C: The heat source is removed but the internal energy of the gas falls to allow the gas to continue expanding while cooling (lowering in temparature). This stage is called abdiatic expansion since no heat enters or leaves the gas.
-U=-W
From C-D: The gas is compressed as heat is extracted and the gas volume decreases. The pressure increases. the gas loses heat to the surroundings. This is an isothermal compression.
W=-Q
From D-A: The internal energy of the gas continues to be compressed. Its temperature rises to its original state whilst its volume decreases because work is done on gas. This is an abdiatic compression.
U=W
It can be shown for an ideal gas undergoing a carnot cycle that the thermal efficiency is given by.
thermal efficieny= Temperature hot reservoir - Temperature cold reservoir / Temperature hot reservoir