Transmission Of Heat Question 109
Question: A solid cube and a solid sphere of the same material have equal surface area. Both are at the same temperature $ 120^{o}C $ , then
[MP PET 1992, 96; MP PMT 2000]
Options:
A) Both the cube and the sphere cool down at the same rate
B) The cube cools down faster than the sphere
C) The sphere cools down faster than the cube
D) Whichever is having more mass will cool down faster
Show Answer
Answer:
Correct Answer: B
Solution:
Rate of cooling of a body $ R=\frac{\Delta \theta }{t}=\frac{A\varepsilon \sigma (T^{4}-T _{0}^{4})}{mc} $
Therefore $ R\propto \frac{A}{m}\propto \frac{\text{Area}}{\text{Volume}} $
Therefore For the same surface area. $ R\propto \frac{1}{\text{Volume}} $ Q Volume of cube < Volume of sphere
Therefore $ R _{Cube}>R _{Sphere} $ i.e. cube, cools down with faster rate.
BETA
