entropy  Consider  any  reversible  cycle,  as  represented by closed  loop in the indicator diagram shown in the fig.e8. We  can  divide  it  into  number  of Carnot cycles. The paths inside  the  figure  will  cancel  out leaving the outer zigzag path. For each carnot cycle the relation,

S [D Q/T] = 0

holds.  If  the  Carnot cycles are made infinitesimally small, the summation can be replaced by integration,

ò [D Q/T] =0

where ò indicates that the integration has been taken over the  closed  path. This  equation  indicates  that ò dQ/T is independent  of  the  path  taken,  and only depends upon the function  at  A,  and B. The function is called entropy, S. We define change in the entropy, S,

D S = S_A- S_B= ò dQ/T

The  addition  of  heat  increases  the  entropy. From the molecular  point  of view, the addition of heat increases the random  motion  of  molecules. Therefore the  entropy is a measure of disorder in a system.