The heat transfer by conduction through a thick sphere is given by
A
$${\text{Q}} = \frac{{2\pi {\text{k}}{{\text{r}}_1}{{\text{r}}_2}\left( {{{\text{T}}_1} - {{\text{T}}_2}} \right)}}{{{{\text{r}}_2} - {{\text{r}}_1}}}$$
B
$${\text{Q}} = \frac{{4\pi {\text{k}}{{\text{r}}_1}{{\text{r}}_2}\left( {{{\text{T}}_1} - {{\text{T}}_2}} \right)}}{{{{\text{r}}_2} - {{\text{r}}_1}}}$$
C
$${\text{Q}} = \frac{{6\pi {\text{k}}{{\text{r}}_1}{{\text{r}}_2}\left( {{{\text{T}}_1} - {{\text{T}}_2}} \right)}}{{{{\text{r}}_2} - {{\text{r}}_1}}}$$
D
$${\text{Q}} = \frac{{8\pi {\text{k}}{{\text{r}}_1}{{\text{r}}_2}\left( {{{\text{T}}_1} - {{\text{T}}_2}} \right)}}{{{{\text{r}}_2} - {{\text{r}}_1}}}$$
Correct Answer: $${\text{Q}} = \frac{{4\pi {\text{k}}{{\text{r}}_1}{{\text{r}}_2}\left( {{{\text{T}}_1} - {{\text{T}}_2}} \right)}}{{{{\text{r}}_2} - {{\text{r}}_1}}}$$
The heat transfer by conduction through a thick sphere is given by $${\text{Q}} = \frac{{4\pi {\text{k}}{{\text{r}}_1}{{\text{r}}_2}\left( {{{\text{T}}_1} - {{\text{T}}_2}} \right)}}{{{{\text{r}}_2} - {{\text{r}}_1}}}.$$