system
Given the following post, respond as if you're commenting on Reddit:
human
Does the energy required to heat water increase as the water temperature increases?

First time poster. Sorry if this should have been a physics question.

If I had water that was 10 degrees Celsius, and I wanted to raise it to 20 degrees Celsius it would require the same amount of energy in joules to do so every time correct?

So if I wanted to take that same water and raise it from 20C to 30C, would it require the same amount of energy in joules as the example above?

Practical use:

I'm about to build a solar heating setup for my pool. I built a controller for the water pump that will pump pool water through the heating coils on my roof. The controller has a temperature probe that will sit inside the coils. The controller senses the temperature inside the coils. Once the water reaches a 'high' temp set point the pump starts running. Once the water drops below the 'low' set point in the coil the pump turns off and waits for the water in the coils to warm up again.

I'm trying to figure out if there's an optimal 'high' temp set point I should be aiming for. I can set it up to 99 Celsius. But perhaps it's more optimal to have it cycle at (for example) 60C if the temperature will climb more slowly after that.

The idea being that if that's true, theoretically I'd have better results if the pump cycles more often.
gpt
The heat capacity of water is basically constant in the temperature range you specify. To be technically correct, the heat capacity of water increases over this range, but for what you are describing it is negligible.