A solid sphere and a hollow sphere of the sam | vedclass

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(A) According to Newton's law of cooling,the rate of heat loss $\frac{dQ}{dt}$ depends on the surface area and temperature difference. Since both sphe

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The rate of cooling of the hollow sphere is higher at temperature $T$.

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(A) According to Newton's law of cooling,the rate of heat loss $\frac{dQ}{dt}$ depends on the surface area and temperature difference. Since both spheres have the same radius and material,their surface areas are equal,so $\frac{dQ}{dt}$ is the same for both.We know that $\frac{dQ}{dt} = mc \frac{dT}{dt}$,where $m$ is the mass,$c$ is the specific heat capacity,and $\frac{dT}{dt}$ is the rate of cooling.Therefore,$\frac{dT}{dt} = \frac{1}{mc} \cdot \frac{dQ}{dt}$.Since the material is the same,$c$ is constant. Because the hollow sphere has a smaller mass $(m)$ than the solid sphere,the rate of cooling $\frac{dT}{dt}$ will be higher for the hollow sphere.

$A$ solid sphere and a hollow sphere of the same material and same radius are heated to the same temperature. They are placed in an environment of the same temperature. If the temperature difference between both and the surroundings is $T$,then .......

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