Assume that the solar constant is 1.4 , kW/m^ | vedclass

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(A) The solar constant $S$ is related to the temperature of the sun $T$,the radius of the sun $R$,and the distance from the sun to the earth $d$ by th

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$5800$

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(A) The solar constant $S$ is related to the temperature of the sun $T$,the radius of the sun $R$,and the distance from the sun to the earth $d$ by the formula: $S = \left( \frac{R}{d} ight)^2 \sigma T^4$ Given: $S = 1.4 \, kW/m^2 = 1.4 	imes 10^3 \, W/m^2$ $R = 7 	imes 10^5 \, km = 7 	imes 10^8 \, m$ $d = 1.5 	imes 10^8 \, km = 1.5 	imes 10^{11} \, m$ $\sigma = 5.67 	imes 10^{-8} \, W m^{-2} K^{-4}$ Substituting the values: $1.4 	imes 10^3 = \left( \frac{7 	imes 10^8}{1.5 	imes 10^{11}} ight)^2 	imes 5.67 	imes 10^{-8} 	imes T^4$ $1.4 	imes 10^3 = \left( \frac{7}{1500} ight)^2 	imes 5.67 	imes 10^{-8} 	imes T^4$ $T^4 = \frac{1.4 	imes 10^3 	imes (1500)^2}{49 	imes 5.67 	imes 10^{-8}}$ $T^4 \approx 1.13 	imes 10^{15} \approx 1130 	imes 10^{12}$ $T \approx 5800 \, K$

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