A solid sphere and a hollow sphere of the same material and size are h...
Introduction:
The question compares the cooling rates of a solid sphere and a hollow sphere of the same material and size when they are heated to the same temperature and allowed to cool in the same surroundings. The temperature difference between the body and the surroundings is denoted by T.
Explanation:
To understand why the hollow sphere cools at a faster rate for all values of T, we need to consider the factors that affect the rate of cooling.
Surface Area:
The rate of heat transfer is directly proportional to the surface area. In the case of a hollow sphere, the outer surface area is larger compared to a solid sphere of the same size. This means that the hollow sphere has a larger surface area available for heat transfer, resulting in a faster cooling rate.
Thickness of Material:
The rate of heat transfer through a material is inversely proportional to its thickness. In the case of a hollow sphere, the material thickness is less compared to a solid sphere of the same size. This means that the hollow sphere allows heat to transfer more easily, leading to a faster cooling rate.
Hollow Space:
The hollow space in the hollow sphere acts as an insulating layer, reducing the heat transfer from the inner surface to the outer surface. This means that the inner surface of the hollow sphere will cool down more slowly compared to the outer surface. As a result, the temperature difference between the inner and outer surface of the hollow sphere is larger, leading to a faster cooling rate.
Conclusion:
In conclusion, the hollow sphere cools at a faster rate for all values of T due to its larger surface area, thinner material thickness, and the presence of a hollow space. These factors facilitate more efficient heat transfer, resulting in a faster rate of cooling compared to the solid sphere.