An electric heater supplies heat to a system at a rate of 100 W. If the system performs work at a rate of 75 W, then the rate at which internal energy increases will be: ____.

To find the rate at which the internal energy of the system changes, we use the first law of thermodynamics in its rate (power) form.

$Ė=\mathrm{Q̇}-\mathrm{Ẇ}$

Here:

• Ė (or ΔU̇) is the rate of change of internal energy (units: watts).
• Q̇ is the rate at which heat is added to the system.
• Ẇ is the rate at which the system does work on its surroundings.

From the problem statement:

• The electric heater supplies heat at $100 W$.
• The system performs work at $75 W$.

Substituting these values into the equation:

$Ė=100 W-75 W$

Carry out the subtraction:

$100-75=25$

Thus, the internal energy of the system increases at a rate of 25 W.