An electric heater receives an energy input of 5000 J of electric energy. During this time the heating element is maintained at a constant temperature. What is ${\Delta E_{thermal}}$ for the heater, and what is Q, the energy transfer between the heater's hot heating element and the cooler air?

Electric heater receives an energy input of 5000 J of electric energy.

${\Delta E_{thermal}}$ for the heater.

Q, the energy transfer between the heater's hot heating element and the cooler air.

Assume no other energy transfers.

System: Heater

Surroundings: Electric wires, air

Energy Principle: ${\Delta E_{sys}} = W + Q$ + other energy transfers

Since there is no internal energy change,

${\Delta E_{thermal}} = {\Delta E_{sys}} = 0$

This is a steady-state situation. This means that $E_{sys}$ = 0 and W = 0.

${\Delta E_{sys}} = W + Q$ + electric energy input

Therefore, 0 is equal to the amount of energy that flows from the surroundings into the system, due to a temperature difference between the system and surroundings plus other energy transfers.

$0 = Q + 5000 J$

Solve for Q

$Q = -5000 J$