# Working of the Carnot Cycle

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,

q1-2= u2 – u1+Wt-2

[u2 – u1 = 0 for isothermal process]

= O+wt-2

or  simply                    q1 = p1v1 In v2 / v1 = RT1 In v2 / v1

w1 -2 is the workdone by the system it is positive (v2 > v1).

(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

q2 -3 = u3– u2 + w2 – 3

0= u3-u2+Wz-J

W2-3= (u2-u3)

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. q2 amount of heat is rejected to

sink at a constant temperature T2. 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

q3-4= u4-u3+w3-4

or                                 q2-0 +w3-4  = P3 v3 In u4 / u4

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

q4- 1 = u1 – U4 + W4 -1

0=u1-U4+W4-l

or                                            W4-1=u4-u1.

[Note. Lower case letters are used for 1 kg of the mass of the system.]