Does a 5000-watt heater use twice the energy of a 2500-watt heater. What calculation do I need to do to compare these and answer the question?

It does while it is on. But if it is controlled by a thermostat, it needs to be on only half as long to maintain the same temperature, so the net energy consumption opver time will be the same.

To compare the energy usage between a 5000-watt heater and a 2500-watt heater, we can use the following calculation:

Energy usage = Power (in watts) x Time (in hours)

For the 5000-watt heater:
Energy usage = 5000 watts x Time (in hours)

For the 2500-watt heater:
Energy usage = 2500 watts x Time (in hours)

To determine if the 5000-watt heater uses twice the energy of the 2500-watt heater, we need to compare the energy usage for the same amount of time. Let's assume we compare the energy usage of both heaters over an hour.

For the 5000-watt heater:
Energy usage = 5000 watts x 1 hour = 5000 watt-hours

For the 2500-watt heater:
Energy usage = 2500 watts x 1 hour = 2500 watt-hours

Based on this calculation, the 5000-watt heater uses twice the energy of the 2500-watt heater in one hour.

However, if both heaters are controlled by a thermostat to maintain the same temperature, the higher wattage of the 5000-watt heater means it can heat the room faster. Consequently, it would only need to be on for half the time to maintain the desired temperature when compared to the 2500-watt heater.

In that case, while the 5000-watt heater would use twice the energy per hour when comparing the time they are both on, the net energy consumption over time would be the same assuming they both maintain the same temperature.