Question

In thermal steady state the temperature of two ends of a meter scale are 30 °C and 20 °C. Temperature of the part of the scale at 60 cm from the hot end is ......... .
(A) 25 °C
(B) 24 °C
(C) 23 °C
(D) 22 °C

Answer 1

Hot end is 25°C

Explanation:

Given,

Temperature, $T_1$ = 20 °C

$T_2$ = 30°C

$R_1$= 60 cm

We know that,

$\frac{\Delta T_1}{R_1} + \frac{\Delta T_2}{R_2}$ = 0

$\frac{ T - 20}{R_1} + \frac{T - 30}{R_1}$ = 0

$T - 20 + T - 30 = 0$

$2T = 50$

$T = 25$

Hot end is 25°C

Answer 2

Given :

The temperature of the hot end = 30°C

The temperature of the another end = 20°C

To find :

The temperature of the part of the scale at 60 cm from the hot end .

Solution :

let the temperature at the part of the scale at 60 cm from the hot end be x°C .

then ,

( 30 - x ) / 60 = ( x - 20 ) / ( 100 - 60 )

=> ( 30 - x ) / 60 = ( x - 20 ) / 40

=> 120 - 4x = 6x - 120

=> 10x = 240

=> x = 24

The temperature of the part of the scale at 60 cm from the hot end is 24°C .