A calorimeter is made of aluminum, shaped as an open-top cube of side length 15.0 cm, with a wall thickness of 2.00 mm. This calorimeter is filled with 300 mL of water, and the whole system is originally at thermal equilibrium at 20.0 degrees C (this is also the temperature of the surroundings).
(a) A small block of copper (m = 30.0 g) originally at 300 degrees C is placed into the calorimeter. Assuming that there is no heat exchange with the surroundings, what is the final equilibrium temperature of the system?
(b) Using Newton's Law of cooling, calculate how long it takes for the entire system to cool to room temperature. You can use the following relationship: T(t) = T0 * e^(-t/tau), where tau is the time constant of the system, which can be approximated using the relationship tau = Cwater/(hA); where C is the heat capacity of water (not specific heat), h is the heat transfer coefficient (take h = 500 W/m^2K), and A is the surface area of the container (4 sides and top).
(c) Now let's see if the assumption of no heat exchange with the surroundings was correct. Calculate the amount of energy transferred via conduction through the 4 sides of the calorimeter in the amount of time you determined in (b).
(d) Calculate the amount of energy transferred via radiation through the surface of water (remember the calorimeter is open on top) in the amount of time you determined in (b).
(e) Can heat exchange with surroundings be ignored?