Examples

Example: An Electric Heater

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?

Facts

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

Lacking

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

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

Approximations & Assumptions

Assume no other energy transfers.

Representations

System: Heater

Surroundings: Electric wires, air

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

Solution

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.

$0 = Q + 5000J$​

Solve for Q

$Q = - 5000J$​