My book describes surface tension as $e=dW/dA$ and work as being negative when it is done against a force. Therefore, if i increase the surface area of a liquid i am doing work on the liquid against the elasticity. My work (dW) should be negative. The increase in area is positive, so the surface tension e should be negative if my work is to be negative dW=edA.
Asked
Active
Viewed 999 times
1
-
2The $dW$ in the equation is the work done on the liquid as the area increases, and this is positive. Working out the sign of work is always a bit of a headscratcher, but look at it this way. The energy of the surface increases as its area increases, so the work done on the surface must be positive so it adds to the surface energy. – John Rennie Feb 02 '16 at 12:19
-
Surface tension is also defined as force per unit length, which clearly can't be negative. – Carl Witthoft Feb 02 '16 at 14:15
-
Or, think if it this way: if the liquid could gain energy by creating surface area, it would be happy to become all surface and no bulk - i.e. not a liquid anymore. – Jon Custer Feb 02 '16 at 15:32
-
Well, technically one could define the work on a system as negative(positive) so long as they are consistent and define the work done by the system as positive(negative) and they keep the signs of other energy terms consistent... In some sense it is a matter of choice but as the previous comments point out, there are physically significant reasons for choosing the work here to be positive. – honeste_vivere Feb 02 '16 at 15:39