Question

A cylinder, a cube, and a sphere, all are made of the same material and having the same mass. If all are heated to a temperature of 150°C, then which will take maximum time to reach 25°C when all are kept at room temperature?
1. Sphere
2. Cylinder
3. Cube
4. All will take equal time.

Answer 1

Correct Answer - Option 1 : Sphere

CONCEPT:

• Heat always flows from a hot to a cold body.
• A body at a temperature higher than its surrounding cools down by giving away the heat to the surrounding and a body at a temperature lower than its surrounding warms up by taking heat from the surrounding.
• The rate at which the body losses heat is directly proportional to the surface area of the body.
• The rate at which a body loses heat to the surrounding is given by Newton's law of cooling.

Newton’s law of cooling

• According to Newton’s law of cooling, the rate of loss of heat from a body is directly proportional to the difference in the temperature of the body, and its surroundings.
• Mathematically it is given as,

\(\Rightarrow \frac{T_1-T_2}{t} = k\left [ \frac{T_1+T_2}{2} - T_s \right ]\)

Where T1 = temperature before cooling, T2 = temperature after cooling, Ts = temperature of surrounding, t = time required and 

k = Positive constant that depends on the area and nature of the surface of the body under consideration

EXPLANATION:

• Since the cylinder, the cube, and the sphere are at the same temperature of 150°C. So the time required to cool from 150°C to 25°C will be maximum for the body for which the heat transfer rate is minimum.
• Since the rate at which the body losses heat is directly proportional to the surface area of the body. So the body which has minimum surface area will lose heat at a minimum rate.
• We know that for the same mass, the surface area of the sphere is minimum. Therefore the sphere will lose heat at the minimum rate compare to the cube and the cylinder.
• So the sphere will take maximum time to cool from 150°C to 25°C.
• Hence, option 1 is correct.