Answer to Question #241477 in Physics for Precious

Question

A copper rod is 81cm in length,has an unknown diameter in millimeter scale,and is used to poke a fire on the surface of the earth.If the temperature on the other end of the rod is maintained at 105 degrees celsius and the cool end has a constant temperature of 21 degrees celsius,what is the temperature of the rod 25cm from the cool end?

A) 47 degrees celcius

B )21 degrees celcius

C)no option is correct

D) 10 degrees celcius

Answer 1

The heat gradient in a rod

$$\frac{\Delta t}{\Delta l}=\frac{105-21}{81}=1.03\:\rm ^{\circ}{\rm C}/cm$$

Hence,  the temperature of the rod 25cm from the cool end

$$t_2=t_1+\frac{\Delta t}{\Delta l}*\Delta l\\ =21^{\circ}{\rm C}+1.03\:\rm ^{\circ}{\rm C}/cm*25\:\rm cm=47\:\rm ^{\circ}{\rm C}$$

Answer: A