How do I find the amount of time it takes to cool a liquid?

Question

I'm trying to figure out how to find the amount of time it takes to cool a boiling pot of water to 180 degrees Fahrenheit, sitting at room temperature. Is there a simple way of doing this?

Its possible for me to find the amount of energy used in going from 212 degrees to 180, but not quite sure where to go from there.

Thanks

Answer 1

The amount of energy is given by the specific heat formula:

E = cp*M*∆T;

cp for water is 4.28 joule/g*ºK

The time it takes for something to cool off depends on the rate of heat flow, which depends on the thremal resistance of the material separating the water from the room air. The heat flow rate is proportional to temperature difference, which is constantly reducing. The result is an exponential decay formula. If you want to determine this experimentally for the the particular pot and water volume you are dealing with, measure the temperature change for a specific time period. The temperature decay formula will be

T1=T0*e^(-t/tc);

measure T0 at t=0, T1 at time ∆t later, comput tc. Then you can find T for any time, or time for any T.

Answer 2

You can the energy by using the formula Q=mc(delta T), where m is the mass of the water, c is the latent heat of water, and delta T is the change in temperature. Make sure you convert the temperature into Celsius or Kelvins. Then you can use the formula P=W/t, where P is power of the stove, W is the work, which is equal to the energy, and t is time. Rearrange the equation to solve for time.

Answer 3

You could always experiment and do several trials to figure out the average.