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(B) Given: Surface area $A = 7 	imes 10^{-2} \,m^{2}$,Mass $m = 300 \,g$,Calorific value $CV = 30 \,kJ/g$,Efficiency $\eta = 10\% = 0.1$,$T_{surface}

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(B) Given: Surface area $A = 7 	imes 10^{-2} \,m^{2}$,Mass $m = 300 \,g$,Calorific value $CV = 30 \,kJ/g$,Efficiency $\eta = 10\% = 0.1$,$T_{surface} = 60^{\circ}C = 333 \,K$,$T_{room} = 0^{\circ}C = 273 \,K$,Stefan-Boltzmann constant $\sigma \approx 5.67 	imes 10^{-8} \,W/m^{2}K^{4}$.The rate of heat loss by radiation (Stefan-Boltzmann Law) is given by $P = e A \sigma (T_{surface}^{4} - T_{room}^{4})$.Assuming $e = 1$ for a black body:$P = 1 	imes (7 	imes 10^{-2}) 	imes (5.67 	imes 10^{-8}) 	imes (333^{4} - 273^{4})$.$P = 3.969 	imes 10^{-9} 	imes (1.230 	imes 10^{10} - 0.556 	imes 10^{10}) \approx 3.969 	imes 10^{-9} 	imes 0.674 	imes 10^{10} \approx 26.75 \,W$.Total heat energy available $H = \eta 	imes m 	imes CV = 0.1 	imes 300 \,g 	imes 30 \,kJ/g = 900 \,kJ = 9 	imes 10^{5} \,J$.The duration $t$ is given by $t = H / P$.$t = (9 	imes 10^{5} \,J) / (26.75 \,W) \approx 33645 \,s$.Converting to hours: $t = 33645 / 3600 \approx 9.35 \,h$.Rounding to the nearest reasonable estimate,$t \approx 10 \,h$.

Similar Questions

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