During a cell culture experiment, a student placed a Petri dish initially at 25°C in an incubator at 40°C. It took 4 hrs for the Petri dish to reach 37°C. After the Petri dish reached 37°C, the student took it out of the incubator and placed it in a water bath at 20°C. How long will it take for the Petri dish to reach 30°C. You can assume that for both processes, the heat transfer can be modeled by Q = -k (T- Tamb), where Tamb = Temperature of the surroundings. k is the heat transfer co-efficient. [Hint: You do not need a value of k or the mass of the Petri dish to arrive at your final answer].
First, please assume the heat transfer coefficient (k) is the same for both air and water. Realistically they are not the same, but they can be approximated to be equal for this problem. Second, one cannot assume rate of heat transfer is the same in each case. The rate of heat transfer will depend on intial and ending temperatures as well as the solution to the governing equations: Q = mCp(dT/dt) and Q = -k(T-Tamb).