Question

2 solid spheres A and B made of same material have radii r and R respectively. both the spheres are cooled from the same temperature under conditions valid for newtons law of cooling . the rate of change in temperature is

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{From}\mathrm{Newton}\text{'}\mathrm{s}\mathrm{law}\mathrm{of}\mathrm{cooling},\mathrm{rate}\mathrm{of}\mathrm{change}\mathrm{of}\mathrm{temperature}, \\ \frac{\mathrm{d\theta }}{\mathrm{dt}}\mathrm{\alpha }\frac{1}{\mathrm{r}} \\ \frac{{\left(\frac{\mathrm{d\theta }}{\mathrm{dt}}\right)}_{\mathrm{A}}}{{\left(\frac{\mathrm{d\theta }}{\mathrm{dt}}\right)}_{\mathrm{B}}}=\frac{{\mathrm{r}}_{\mathrm{B}}}{{\mathrm{r}}_{\mathrm{A}}} \end{gathered}$$