# Newton's Law of Cooling temp graph

## Main Question or Discussion Point

Hi,
I'm thinking of doing an experiment related to Newton's law of cooling, just a simple heat up a liquid to a temp graph its rate of cooling, repeat for different liquids. I was thinking of seeing if from this graph I could calculate the specific heat capacity of the liquid, but I don't know if there is a link between K and C and whether they can be found from a graph. I was also wondering if to get more complex maths involved there are and related integral or differential calculations that would be worth doing on the graph or equations?
Q=mcT
T2 = T0 + (T1 - T0) * e(-k * Δt)
B

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What is K? What is C?

The other aspects you need to consider are:
1) Newton's Law of Cooling applies when the substance has a temperature which is very close to temperature of surroundings. How do you plan to maintain that?
2) The liquid will be arranged in some sort of container, which will allow heat to flow out due to conduction. Hence the values you get will not be the value of heat lost by liquid, but only a part of it.
3) The experiment will have to be done hundreds of times to get anything close to a good approximation. (My textbook says Joule worked twenty years paddling a foot pedal to verify the First Law of Thermodynamics- I dunno how far it is true, but I am sure we don't have such a timescale here).

I am sorry if that discourages you but hey, if everyone could do experiments so easily we wouldn't need CERN. Its always worth trying though, in keeping with the scientific spirit.

russ_watters
Mentor
In order to find C (heat capacity) you need to know K (heat transfer coefficient). This can be extremely difficult, but you can help matters by insulating and sealing the container. A sheet of styrofoam insulation has known thermal conductivity and all but eliminates other heat transfer modes. Then you can test something with a known heat capacity to calibrate the system and then test other objects/substances.