Why define entropy with heat instead of work?

[Andrew U]

From what I understand, in the Carnot cycle summing qi/Ti for each step results in zero, thus indicating a new state function, entropy = qrev/T. But since dE = 0 = q+w, then q = -w, and looking at the equations derived from the cycle summing wi/Ti for each step should also result in zero. So why can't one also define entropy as wrev/T?

 

[Chestermiller]

Suppose you heat a body without doing any work. Does its entropy change?