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 $



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