Question

A uniform thermometer scale is at steady state with it's 0cm mark at 20°c and 100cm mark at 100°c.temperature of the 60 cm mark is

Answer 1

use formula , $\theta=\frac{l_{\theta}-l_0}{l_{100}-l_0}\times(\theta_b-\theta_m)$
here ,$\theta_b=100^{\circ}C$ and $\theta_m=20^{\circ}C$
so, formula converted into ,
$\theta=\frac{l_{\theta}-l_0}{l_{100}-l_0}\times80$

where $l_{\theta}$ is the mark at $\theta^{\circ}C$ , $l_0$ is the mark at 20°C , $l_{100}$ is the mark at 100°C.

$\text{Given},l_0=0cm,l_{100}=100cm,l_{\theta}=60cm$

so, $\theta=\frac{60-0}{100-0}\times80$

$\theta=48^{\circ}C$

Answer 2

As 60cm is at distance of 60 from the 0 cm mark and 40 from the 100cm mark; by applying the formula of conduction

(T - 20)/60 = (100 - T)/40

4T - 80 = 600 - 6T

T = 68 C