# Predicting the temperature of an object using the heat of its surroundings after a certain amount of time?

how would you predict what the temperature of something would be if it spends a certain amount of time exposed to heat from its surroundings? is this possible?

ex. what temperature would a hot bottle of water at initial temp 48 C be after being put in a 4 C refrigerator for 2 hours?

• The calculations are possible, but pretty complicated. May 21 '18 at 5:00
• As @Ivan Neretin comments you will need to use Fick's laws of diffusion, and know all the thermal diffusion coefficients etc. for the materials used. This will be a calculation that will have to be done numerically and would be standard-ish if you were a chemical engineer. In fact I suspect that it will be quicker and more accurate to do an experiment. May 21 '18 at 6:53
• Sure. Start here. You can make quick and moderately accurate estimates with some simplifying assumptions about your system. May 21 '18 at 8:49

You're basically looking at radiation, conduction, and convention as methods to dissipate heat.

Heat loss by radiation can be computed from Wein's law or something similar.

Conduction requires knowing the thermal properties and dimensions of the materials in contact.

Convection is the trickiest one since it requires some model for how the air or other fluid around the object is moving and coupling this to conduction.

All three are subject to significant errors in computation if you're not careful though if you're trying to estimate rough order of magnitude, you might not care.

All in all, this is not an easy problem to compute from first principles.

Note also that your example is not nearly well-defined enough to solve this problem. What is the surface area of the bottle and the size of the refrigerator. How well does the refrigerator maintain its internal temperature? Is there a fan? Is the water inside a thermos bottle?