The working of Carnot cycle is shown in Figs. 7.1 & 7.2 on P-v diagram. The sequence of operations is described below.

(1) State 1 is having initial volume and initial pressure of the 1 kg mass system in the cylinder.

Now the cylinder head is a perfect conductor of heat and q1 quantity of heat at T1 (source temperature) is supplied to system of the engine cylinder till the state 2 is reached. The volume of the system increases and isothermal expansion process 1 – 2 takes place. At point 2, the supply of heat is cut off.

For process 1 – 2 we apply 1st law,

q_{1-2}= u_{2} – u_{1}+W_{t-2}

_{2}– u

_{1}= 0 for isothermal process]

= O+w_{t-2}

or simply q_{1} = p_{1}v_{1} In v_{2} / v_{1} = RT_{1} In v_{2} / v_{1}

w_{1 -2} is the workdone by the system it is positive (v_{2} > v_{1}).

(2) At the point 2, cylinder head is changed to insulator. During the process 2 – 3, the

heat source is removed, the system expands reversibly and adiabatically till its

temperature falls to T _{2}.

For process 2 – 3

q_{2 -3} = u_{3}– u_{2} + w_{2} _{– 3}

0= u_{3}-u_{2}+Wz-J

W_{2-3}= (u_{2}-u_{3})

work w2-3 is done by the system at the expense or decrease in internal energy.

(3) The cylinder head is changed to conductor of heat. q_{2} amount of heat is rejected to

sink at a constant temperature T_{2}. The process 3-4 is now followed and it is again

isothermal heat rejection to sink.

The work during the 3 – 4 process is given by

q_{3-4}= u_{4}-u_{3}+w_{3-4}

or q_{2-0} +w_{3-4} = P_{3} v_{3} In u_{4} / u_{4}

This w3 – 4 is done on the system. . .. (7.2)

(4) The cylinder head is again changed to insulator and adiabatic compression is done

to bring back to state 1. The cycle is completed.

During process 4 – 1 the work done on the system is given by

q_{4- 1 }= u_{1} – U_{4 }+ W_{4 -1}

0=u_{1}-U_{4}+W_{4-l}

or W_{4-1}=u_{4}-u_{1}.