working of Carnot cycle

This cycle consists of two adiabatic and two isothermal processes, as shown in the P-V and T-S diagrams of the Fig. (a) & (b).

Air is assumed to be the working fluid, which is contained in a cylinder. The walls of this cylinder are made up of some non-conducting (Insulating) materials The cylinder cover which is also made of non-conducting material can be removed or placed on the cylinder head as and when required.

      1 At point ‘a’: The pressure volume and temperature of air at ‘a’ be P1V1 and T1 respectively.

      A hot body at temperature T1 is brought in contact with cylinder end (cylinder head) The air expands isothermally to point ‘b absorbing heat from the hot body Due to expansion of the air, the piston is forced out, thus doing some useful work

      2. At point ‘b’: The hot body is removed and the end of the cylinder is covered with the non-conducting cover The air at point ‘b’ expands adiabatically to point c. During adiabatic expansion the temperature of the air decreases and at the same time work is done At point ‘c’ let the temperature of air be ‘T2’

      3 At point ‘c’: The cold body at temperature T2 is brought in contact with the cylinder end in place of non-conducting cover The air s compressed isothermally to point ‘d rejecting heat to the cold body

      4 At point‘d’: The cold body is removed and again the cylinder end is covered with the non-conducting cover. The air is compressed adiabatically to point ‘a’. The temperature of the air rises from T2 to T1 This way the cycle is completed

       Now let P1, V1 and T1 be the pressure volume and temperature of air at point ‘a’ and P2, V2 and T2 their corresponding values at point ‘c’.

Also let there be only one kg of air in the cylinder.

The value of expansion ratio and compression ratio must be equal, otherwise the cycle will not close.

      According to law of conservation of energy;

                                      Work done = Heat supplied — Heat rejected

...........................(1)

From equation (1), it is clear that the efficiency of the cycle depends upon the temperature range only. No other property of the working fluid (air) affects it.