A very large swimming pool filled with water of temperature equal to $20\ \mathrm{^\circ C}$ is heated by a resistor with a heating power of $500\ \mathrm{W}$ for $20$ minutes. Assuming the water in the pool is not in any contact with anything besides the resistor:
Is the change of entropy of the resistor positive, negative, or zero?
My Attempt
Entropy is given by the formula: $\mathrm dS = \frac{q_\text{rev}}{T}$
My first thought was that since the resistor is giving off heat energy to the water, $q$ must be negative and therefore the entropy change must be negative. However, does the fact that there is a continuous current of electrons passing through the resistor complicate this simple calculation? I am thinking that the current of electrons increase the entropy of the resistor and offsets the decrease in entropy due to heat loss. Am I correct?
The answer in the book is that the entropy change is $0$.