A liter of water, initially at 30°C is placed in a refrigerator set to 5°C.
a. Write the equation to find the time it takes a liter of water to cool 7°C, as a function of thermal resistance.
b. Plot the time it takes a liter of water to cool as a function of thermal resistance, where the thermal resistance varies between just above zero to near infinity.
c. Assuming the temperature of the water in the system is everywhere uniform, do you expect that the water will cool faster (i) in an aluminium container or a plastic container and (ii) in a spherical container or a tall, narrow cylindrical container? Explain your rationale for your answer to both part (i) and (iii)