Transmission Of Heat Question 98
Question: Ice starts forming in lake with water at $ 0^{o}C $ and when the atmospheric temperature is $ -10^{o}C $ . If the time taken for 1 cm of ice be 7 hours, then the time taken for the thickness of ice to change from 1 cm to 2 cm is
[NCERT 1971; MP PMT/PET 1988; UPSEAT 1996]
Options:
A) 7 hours
B) 14 hours
C) Less than 7 hours
D) More than 7 hours
Show Answer
Answer:
Correct Answer: D
Solution:
$ t=\frac{\rho L}{2K\theta }(x _{1}^{2}-x _{2}^{2}) $
Therefore $ t\propto (x _{2}^{2}-x _{1}^{2}) $
Therefore $ \frac{t}{t’}=\frac{(x_2^{2}-x_1^{2})}{(x’_2^{2}-x’_1^{2})} $
Therefore $ \frac{9}{t’}=\frac{(1^{2}-0^{2})}{(2^{2}-1^{2})} $
Therefore $ t’=21,hours $
BETA
