PHYSICS · Multi-part · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter
Problem
A cylindrical metal rod, initially heated to 160∘C, is placed in a room whose air temperature is held constant at 22∘C. Let T(t) (in ∘C) denote the temperature of the rod t minutes after it is placed in the room.
Experimental observations show that the instantaneous rate of change T′(t) is proportional to the difference T(t)−22 at every moment.
(a) Without performing any explicit calculations, describe the sign of T′(t) for all t≥0 and explain what this indicates about the rod’s temperature over time.
(b) Explain why the quantity T(t)−22 must approach 0 as t→∞. Relate your reasoning to the physical context of the problem.
(c) Suppose a second identical rod is removed from the oven at the same initial temperature and placed in the room exactly 10 minutes later. Compare, without calculation, the values of T′(12) for the first rod and the second rod, and justify your comparison.