NEET Solved Paper 2014 Question 16
Question: Certain quantity of water cools from $ 70^{o}C $ to $ 60^{o}C $ in the first 5 min and to $ 54^{o}C $ in the next 5 min. The temperature of the surroundings is [AIPMT 2014]
Options:
A) $ 45^{o}C $
B) $ 20^{o}C $
C) $ 42^{o}C $
D) $ 10^{o}C $
Show Answer
Answer:
Correct Answer: A
Solution:
Let the temperature of the surrounding is $ t^{o}C $ .
For first case, $ \frac{(70-60)}{5\min }=k({65^{{}^\circ }}C-{t^{{}^\circ }}C) $ ( $ 65^{o} $ is average of $ 70^{o}C $ and $ 60^{o}C $ )
$ \frac{10}{5\min }=K({65^{{}^\circ }}C-{t^{{}^\circ }}C),…..(i) $
For second case, $ \frac{(60-54)}{5\min }=k(57-t)…..(ii) $
( $ 57^{o}C $ is average of $ 60^{o}C $ and $ 54^{o}C $ ) From Eqs. (i)/(ii), $ \frac{10}{6}=\frac{(65-t)}{(57-t)} $
Solving, we get $ t=45^{o}C $
