Temperature v. Time: Mixing hot and cold water in the same cup allows them to rapidly reach equilibrium

The theoretical final temperature of the water is 47.7 degrees celsius.


Below is the theoretical value for the specific heat of Aluminum along the the calculation for the uncertainty of this value.

The theoretical value for the specific heat of aluminum is 2810 J/kg * K +- 3.720

Temperature v. Time: A can holding cold water submerged into a styrofoam cup of hot water does not reach equilibrium as fast. There is an exponential decay in temperature for the hot water.

Reasons why the final temperature was much lower than when hot and cold water were mixed directly

Reasons for the longer time to reach equilibrium

These variables directly effect the rate of heat flow

A graph of the energy transfer into water. For the majority of the transfer, there is a linear relationship between temperature and time.

Activity representing the transfer of energy. Two rods of different materials held together. One end is in boiling water, the other is in an ice bath.

       
 Summary: The amount of energy transferred depends on the mass, the material of the mass, and the change in temperature. The transfer of heat depends on the length through which energy travel, the material through which its traveling, the change in temperature, and the cross sectional area of transfer. The rate of transfer is also equal throughout the whole system. The actual value for the specific heat of aluminum is 9100 J/kg * K, which is 3 times the value is calculated the specific heat to be. This could be due to the elevation being slightly less than 1 atm, the equipment used to measure mass and temperature not being calibrated, and the estimation of the weight of the aluminum can.