Can an Oven being set to a different temperature cause electric board to go off?

Question

Basically: the electrical system kept going off (when light goes down in a division due to too many electrical appliances on at a time, or their combined power consumption).

My roommate said it was because I had the oven at 250º.

I said it didn't matter, because the Oven was either on, trying to reach the desired temperature, or off, if it was near, or at that temperature.

We kept arguing and got nowhere.

Does an Oven being set to 30ºC, or 250ºC, matter for the sake of the electrical board fuse going off?

My stance is that it's either ON, or OFF, if it's at the temperature, or not. So my side is that it's either consuming nothing (0w), or it's needed wattage.

Am I right? If so, how can I explain it to him?

Answer 1

The walls of the oven are not perfect insulators. Heat will escape through them. The heat equation, which is (in 1d):

$$ \frac{dT}{dt} = \alpha \frac{d^2 T}{dx^2} $$

Here $\alpha$ describes how good the material is at conducting heat; higher $\alpha$ means quicker heat transfer. $T$ is the temperature. The left hand side is a measure of how quickly the temperature is changing, and the right hand side is a measure of how drastic the temperature difference is as you move along the $x$ direction (in this case, as you move from the inside to the outside of the oven wall).

This tells you that the rate of heat loss increases as temperature on one side of the oven wall increases. So maintaining a higher temperature would require higher wattage. Also, note that watts are units of power, which is energy/time, so you you should just say watts, not watts/per time.

Of course, this is in the steady state (once the oven has been preheated). When the oven is first turned on, it is very possible that it is using maximum power just to get itself heated up, meaning that the power used (in watts) might only depend on temperature once the oven has been preheated. But, once it reaches the set temperature, its wattage really will increase with increasing temperature.

But if you're worried about blowing fuses, then it is likely (depending on the design) that it will use maximum power from the moment it turns on, regardless of set temperature, until it preheats. So for blowing fuses, my guess is that it wouldn't matter.

Answer 2

A simple model of a simple oven:

The oven is an imperfectly heat insulated cavity, equipped with a simple ON/OFF thermostat controlling the current $I$ flowing through a series of electrical heating elements with power $P$. As long as the oven temperature $T_{oven}$ is lower than the set temperature $T_{set}$ full power $P$ is delivered to the oven.

Once $T_{oven} \geq T_{set}$ the thermostat switches OFF the heating. The hot heating elements will still deliver some residual power for a short while, so that $T_{oven}$ will slightly overshoot $T_{set}$.

As the oven is insulated but not perfectly it constantly loses heat energy (Enthalpy), represented by $Q_{loss}$ and this causes $T_{oven}$ to decrease, until it drops below the set temperature: $T_{oven} <T_{set}$, at which point the current is switched ON again. As long as $P>Q_{loss}$ the oven temperature will start to rise again and the cycle repeats itself.

The actual power used over prolonged periods of time is in fact $Q_{loss}$ and since as (Newton's Cooing Law): $$Q_{loss} \propto T_{set}-T_{amb}$$

Where $T_{amb}$ is the ambient temperature.

So higher set temperatures do cost more electrical energy.