Question

Two rectangular blocks can be arranged either in configuration 1 or in configuration?As shown in fig.
It takes 9 seconds to transfer a certain amlt of heat from hot end to cold end in configuration 1. the time to transport some of amt of heat in configuration?

Answer 1

Given Date

$r_1=\frac{L}{kA}$

$r_2=\frac{L}{2kA}$

For configuration $\left(i\right)$

$r^1=r_1+r_2$

$=\frac{L}{k\pi }+\frac{L}{2kA}=\frac{L}{3kA}$

For configuration $\left(ii\right)$

$r^{11}=\frac{r_1{r}_2}{r_1+r_2}=\frac{\frac{L}{kA}.\frac{L}{2kA}}{\frac{L}{kA}+\frac{L}{2kA}}=\frac{L^2}{2k^{2}A}\times \frac{2kA}{3L}=\frac{L}{3kA}$

Now $\frac{△Q}{k}=\frac{△t}{r}=\frac{t_{\left(i\right)}}{t_{\left(ii\right)}}=\frac{n^1}{r^{11}}$

$t_{\left(ii\right)}=\frac{r^{11}}{r^1}\left(t_{ii}\right)\frac{\frac{L}{3kA}}{\frac{3L}{2kA}}\times 9=\frac{L}{3kA}\times \frac{2kA}{3L}\times 9=2sec$

$t_{\left(ii\right)}=2sec$

Time for second configuration $tsec$