Apply the first law of thermodynamics to a resistor carrying a current i. Identify which of the quantities ΔQ, ΔU and ΔW are zero, which are positive and which are negative.

First law of thermodynamics states –

the total energy of an isolated system is constant, energy can neither created nor destroyed, but can be transformed from one form to another

where

ΔU is the change in the internal energy,

∆Q is the heat added to the system,

and ∆W is the work done by the system.

Now, here the battery is doing positive work on a resistor carrying current i.

Thus, ∆W is positive.

The work done on the resistor is used to increase its thermal energy in the form of heat, thus ∆Q is positive.

As the temperature of the resistor rises, ΔU is positive.