Respuesta :
It takes 126 s for the sphere to cool by 1K
Calculation
Density pf copper = 8900
Radius of sphere = 5cm
emissivity = 1
initial temperature = T=300K
we know [tex]\delta[/tex]t = [tex]\frac{\delta Q}{H}[/tex] = [tex]\frac{mc \delta T}{A \sigma e T^4}[/tex]
We can express it as
m = [tex]\rho V[/tex]
A = 4[tex]R^{2} \pi[/tex]
[tex]\delta t = \frac{\rho Vc \delta T}{4R^2 \pi \sigma e T^4}[/tex]
Volume V = 4/3 [tex]R^{2}\pi[/tex][tex]\delta t = \frac{\rho 4/3 R^3\pi c \delta T}{4R^2\pi \sigma e T^4}[/tex]
[tex]\delta t = \frac{\rho Rc \delta T}{3 \sigma e T^4}[/tex]
[tex]\delta t[/tex] = [tex]\frac{8900*0.05*390*1}{3*5.67*10^{-8}*1*300^4}[/tex]
[tex]\delta t[/tex] = 126s
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