So I'm trying to come up with a simple hack to heat up food in a water bath to hopefully +-1ºC of a target temperature, but I really don't understand the physics of it all so much. I'm pretty sure I can keep a hot plate at a somewhat steady temperature by cycling it on an off at regular intervals, but I'm not sure what that means for the food itself.
Here's what I'm thinking: If I can get the hot plate to stay steady at a temperature of my choice, when will place a pot of water on it and the water will stop heating up after it hits some lower temperature point, say at 75ºC. That means it has reached thermal equilibrium and is heating up at the same rate as it loses heat to the environment - and as long as the heat output of the plate is the same and the environment is stable, the water shouldn't drastically change temperature.
What I want to know is: will the final equilibrium temperature will be significantly different after putting some food in it?
I did some googling and managed to come with the following, probably wildly incorrect reasoning:
Most foods' specific heat is around 3 kJ/KgºC, and waters' is around 4 kJ/KgºC. I suppose that means given the same heat input, food will heat up about 1.33x more than water?
And thus a pot with, say, 3kg water and 1kg of meat (assuming a specific heat of 3 kJ/KgºC for the meat), all the stuff in the pot will have an average specific heat of 3.25 kJ/KgºC (3+3+3+4=13, divided by 4kg = 3.25), so it will all heat up 1.08x more?
What exactly does heating up 1.08x more mean, though? Do I just multiply 75ºC by 1.08? Surely not, right? Do I need to stick 1.08 in some formula or convert it to kelvin or something? What even are numbers, really? Thanks!
Just to clarify, what I'm concerned here is the final temperature once the pot reaches equilibrium again, not how much the temperature will drop when the food is added.
EDIT: To further clarify - what I want to calculate is what the final equilibrium temperature of a pot of water will be after placing some food in it, knowing only the final equilibrium temperature of the water before placing the food.