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JEE Main & Advanced Physics Thermometry, Calorimetry & Thermal Expansion Question Bank Self Evaluation Test - Thermal Properties of Matter

  • question_answer
    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 \[\left[ \sigma = 5.67\times 1{{0}^{-8}}\frac{Joule}{{{m}^{2}}\times sec\times {{K}^{2}}} \right]\]         

    A) 108 joule

    B) 168 joule

    C) 182 joule

    D) 192 joule

    Correct Answer: C

    Solution :

    [c] According to Stefan's Law, the rate of loss of heat is \[\frac{Q}{t}=\sigma A\left( T_{1}^{4}-T_{2}^{4} \right)\times e\] here \[\sigma =5.67\times {{10}^{-8}}/{{m}^{2}}\times sec.{{K}^{2}},\] \[{{\operatorname{T}}_{1}}=527+273=800K,\] \[{{\operatorname{T}}_{2}}=27+273=300K\And A=200\times l{{0}^{-\,4}}{{m}^{2}}\] 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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