Transmission Of Heat Question 344
Question: A metallic sphere having radius 0.08 m and mass m = 10 kg is heated to a temperature of $ 227{}^\circ C $ and suspended inside a box whose walls are at a temperature of $ 27{}^\circ C $ . The maximum rate at which its temperature will fall, is (Take $ e=1, $ Stefan’s constant $ \sigma =5.8\times {{10}^{-8}}W{{m}^{-2}}{{K}^{-4}} $ and specific heat of the metal $ s=90,cal/kg/\deg ,,J=4.2 $ joules/calorie)
Options:
A) $ {{0.055}^{o}}C/s $
B) $ {{0.066}^{o}}C/s $
C) $ {{0.044}^{o}}C/s $
D) $ {{0.033}^{o}}C/s $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Rate of heat loss $ =\sigma eA(T^{4}-T _{s}^{4}) $
$ -ms\frac{dT}{dt}=\sigma eA(T^{4}-T _{s}^{4}) $
$ -\frac{dT}{dt}=\frac{5.8\times {{10}^{-4}}\times \pi {{(0.08)}^{2}}[{{(500)}^{4}}-{{(300)}^{4}}]}{10\times 4.2\times 90} $
$ \Rightarrow $ $ \frac{-dT}{dt}={{0.066}^{o}}C/s $
BETA
