# Change of entropy

Homework Statement
A 10 ohms resistor is held at temperature of 300 K. A current of 5 A is passed through the conductor for 2 mins. Ignoring changes in the source of the current, what is the change of entropy in the resistor.

I solved it like this:
$$\Delta S=\int dS=\int\frac{dQ}{T}=\frac{1}{T}\int dQ=\frac{\Delta Q}{T}=\frac{I^2Rt}{T}$$

However, the book says the answer is 0, because temperature is held constant. Well, so is during an isothermal expansion, but there the change of entropy is Rln2. I believe the answer lies in that the isothermal expansion is reversible process, while the dissipation of heat in the conductor isn't, so there the change of entropy must be 0, but can someone explain it in detail.

Mapes
Homework Helper
Gold Member
A better book answer would be that the state of the resistor---temperature, volume, mass---is the same at the beginning and the end of the process, and because entropy is a state variable (i.e., its value depends upon the state only), the entropy change must be zero. The same isn't true for a gas expansion because the volume has changed.

Andrew Mason