A circular plate, a cube and a sphere, all made up of the same material and having the same mass, are heated to 300°C and left in a room. Which of them will have the slowest rate of cooling?
(1) Circular plate
(2) Cube
(3) Sphere
(4) All will cool at the same rate
Answer: (3) In the late 17th-century British scientist Isaac Newton studied the cooling of bodies. Experiments showed that the cooling rate is approximately proportional to the difference in temperatures between the heated body and the environment. This fact can be written as the differential relation :
dQ/dt= αA(Ts-T) where A is the surface area of the
body through which the heat is transferred, T is the temperature of the body, TS is the temperature of the surrounding environment, á is the heat transfer coefficient depending on the geometry of the body, state of the surface, heat transfer mode, and other factors. Surface area or volume ratio is an important influence on temperature control. For the same volume, the sphere has a minimum surface area, while the circular plate has a maximum surface area. So sphere cools slowest and the plate cools fastest.
