A sphere, a cube, and a thin circular plate, all of the same materials and same mass, are initially heated to the same high temperature. (A) The plate will cool fastest and cube the slowest. (B) Spheres will cool fastest and cube the slowest. (C) The plate will cool fastest and sphere the slowest. (D) The cube will cool fastest and plate the slowest.
Hint We have a sphere, a cube, and a circular plate. All are made of the same material and have the same mass. We have to find which of them will cool faster when they are heated to the same high temperature. The cooling will be depending on the shape of the material.
Complete Step by step solution From the given shapes, all of them have the same mass. The circular plate will be having the largest surface area out of the three. This will help the plate to cool down faster. Out of the three, the sphere will be the shape having the minimum surface area for a given volume. Hence the sphere will be cooling down the slowest. Therefore, we can say that the plate will cool the fastest and the sphere the slowest.
The answer is: Option (C): The plate will cool the fastest and the sphere the slowest.
Additional Information The amount of heat required to raise the temperature of any substance through one Kelvin is called the heat capacity of the material. The amount of heat required to raise the temperature of one-kilogram substance through one Kelvin is called the specific heat capacity of the material.
Note The rate of heating and cooling will depend on the surface area of the material. Materials with larger surface areas tend to cool down faster and materials with lesser surface areas will take more time to cool down. We know that for any given volume a sphere will be the shape with the minimum surface area.