The PV cycle for an ideal gas – the Carnot cycle

Tbe concept of the ideal heat engine was first developed by the French scientist Sadi Carnot in 1824. He imagined an engine that was free from friction and where the working substance, usually a gas, was taken through a completely reversible cycle consisting of two isothermal and two adiabatic changes.

Figure 1(a)

AB    ISOTHERMAL EXPANSION at temperature T₁. To keep the temperature constant an amount of heat energy (Q₁) must be ADDED to the gas
BC    ADIABATIC EXPANSION - no heat enters or leaves the system and so the temperature falls from T₁ to T₂.
CD   ISOTHERMAL COMPRESSION at temperature T₂. To keep the temperature constant heat energy (Q₂) must be REMOVED from the gas at a temperature T₂. Notice that T₂ is LESS then T₁.
DA       ADIABATIC COMPRESSION - no heat enters or leaves the system and so the temperature rises from T₂ to T₁
The area in the closed loop is the WORK DONE BY THE GAS

Figure 1(b)

AB    ISOTHERMAL COMPRESSION at temperature T₁. To keep the temperature of the gas constant heat a quantity of heat energy (Q₁) must be REMOVED from the gas at a temperature T₁.
BC    ADIABATIC EXPANSION - no heat enters or leaves the system and so the temperature falls from T₁ to T₂
CD    ISOTHERMAL EXPANSION at temperature T₂. To keep the temperature of the gas constant a quantity of heat energy (Q₂) must be ADDED to the gas at a temperature T₂. Notice that T₂ is LESS then T₁.
DA   ADIABATIC COMPRESSION - no heat enters or leaves the system and so the temperature rises from T₂ to T₁.

The area in the closed loop is the WORK DONE ON THE GAS.

The direction round the loop is all-important. This decides whether the system is operating as a heater or a refrigerator.
The work done by the gas is given by the area ABCYXA and the work done on the gas is given by the area CDAXYC. The net work done by the gas is therefore represented by the area ABCD.