Properties Of Solids And Liquids Question 439
Question: A metal ball of surface area 200 square cm, temperature $ 527{}^\circ C $ is surrounded by a vessel at$ 27{}^\circ C $ . If the emissivity of the metal is 0.4, then the rate of loss of heat from the ball is approximately $ [ \sigma = 5.67\times 1{{0}^{-8}}\frac{Joule}{m^{2}\times sec\times K^{2}} ] $
Options:
A) 108 joule
B) 168 joule
C) 182 joule
D) 192 joule
Show Answer
Answer:
Correct Answer: C
Solution:
[c] According to Stefan’s Law, the rate of loss of heat is $ \frac{Q}{t}=\sigma A( T _{1}^{4}-T _{2}^{4} )\times e $
here $ \sigma =5.67\times {{10}^{-8}}/m^{2}\times sec.K^{2}, $
$ {{T} _{1}}=527+273=800K, $
$ {{T} _{2}}=27+273=300K\And A=200\times l{{0}^{-4}}m^{2} $
So. $ \frac{Q}{t}=5.67\times {{10}^{-8}}\times 2\times l{{0}^{-2}} $
$ [{{(800)}^{4}}-{{(300)}^{4}}]\times 0.4 $
$ \cong 182 joule $
