Why Does a Hollow Sphere Cool Faster Than a Solid Sphere?

[Amith2006]

Sir,
It is said that a hollow sphere cools faster that a solid sphere. Is it because a hollow sphere contains smaller quantity of heat than the solid sphere? Or is it because the rate of heat loss is inversely proportional to thickness of the conductor through which heat is lost?

 

[Hootenanny]

Consider the density of a solid sphere, compared to a hollow sphere; and hence compare the specific heat capacity of the two spheres.

~H

 

[kyle8921]

There are a few factors that contribute to the difference in cooling rates between a hollow sphere and a solid sphere. First, the amount of heat contained within the sphere does play a role. A hollow sphere has a smaller volume than a solid sphere of the same size, so it contains less heat energy. This means that it will cool faster simply because there is less heat to dissipate.

However, the rate of heat loss is also affected by the thickness of the material through which heat is lost. In the case of a hollow sphere, the thickness of the material is smaller compared to a solid sphere. This means that heat can escape more easily from the hollow sphere, leading to a faster rate of cooling.

Additionally, the surface area to volume ratio also plays a role in the rate of cooling. A hollow sphere has a larger surface area compared to its volume, allowing for more surface area available for heat to dissipate. This further increases the rate of cooling compared to a solid sphere.

Overall, it is a combination of these factors that contribute to the faster cooling rate of a hollow sphere compared to a solid sphere.