A uniform metal rod `AB` 80 cm long is heated at the end A and the end B is kept in ice. The temperature of the end A is 100°C and that of the end B is 0°C. The rod is covered with wool such that there is no loss of heat from the surface of the rod. Assuming steady state find (i) the temperature gradient along the rod, (ii) the temperature at a point D distance 60 cm from the end A and (iii) the distance of the point C from the end A where the temperature is 65°C.

Explanation

(i) Temperature gradient `= ( theta_1 - theta_2)/(x )`
`= ( 100-0)/( 80) =1.25^(@) C// "cm"`
(ii) Let the temperature at a point D distant 60 cm from the end A be `theta`.
`(100- theta)/( 60) = 1.25`
`100- theta = 1.25 xx 60 = 75 , theta = 100- 75= 25^(@) C`
(iii) Let the point C at a distance x from the end A
`(100-65)/( x) = 1.25 , 35 = 1.25x, x = (35)/( 1.25) = 28` cm
`35 = 1.25 x`
`x= (35)/( 1.25) = 28` cm