Question

Initial temperature distribution along the length of the rod is given above. Final temperature distribution, after a long time, can be expressed as

• A. T = 75 cos (15.7x)${}^{\circ }$C
• B. T = 25${}^{\circ }$C
• C. T = 25 tan (15.7x)${}^{\circ }$C
• D. T = 0${}^{\circ }$C

Answer 1

The correct option is D T = 0${}^{\circ }$C

Since there is a continuous heat loss from sides (as $\frac{dQ}{dt}\alpha \frac{dT}{dx}$ will increase till middle of rod and then decrease). Hence finally temperature throughout will fall and hence rod will be uniform at $T=0^{o}C$.