Question

Write a mathematical statement for the change in entropy, ds, for the case where no work
is done irrespective of the path

Answer 1

To write:

Mathematical statement for change in entropy , for a thermodynamic change in which no work has been done.

Solution:

Entropy is a thermodynamic parameter referring to to the randomness of molecules within a system. In other words it describes the chaos within a system.

Entropy is calculated from the ratio of of heat change in the system to the absolute temperature of the system.

Let entropy be denoted as S , Internal Energy change be ∆U , T be Absolute Temperature and W be work done ;

$\rm{\Delta S = \dfrac{\Delta Q}{T} }$

Putting 1st law of thermodynamics :

$\rm{ = > \Delta S = \dfrac{\Delta U +W }{T} }$

Since , no work is done by/for the system :

$\rm{ = > \Delta S = \dfrac{\Delta U +(0) }{T} }$

$\rm{ = > \Delta S = \dfrac{\Delta U }{T} }$

So , final answer is :

$\boxed{ \red{ \rm{\Delta S = \dfrac{\Delta U }{T} }}}$