An electric heater supplies heat to a system at a rate of 100 W. If...

According to the first law of thermodynamics:

$\dfrac{dQ}{dt} = \dfrac{dU}{dt} + \dfrac{dW}{dt}$

Given that the rate of heat supplied is $\dfrac{dQ}{dt} = 100$ W and the rate of work done by the system is $\dfrac{dW}{dt} = 75$ J/s = $75$ W.

Substituting the values:

$100 = \dfrac{dU}{dt} + 75$

$\dfrac{dU}{dt} = 100 - 75 = 25$ W

The rate at which internal energy increases is $25$ W.

Answer: $25$ W