Answer:
its surface temperature = 54.84 ° C
Explanation:
The density of aluminium [tex](\rho)[/tex] = 2700 kg/m ³
Heat capacity [tex]( c_p)[/tex] = 897 J/Kg.K
radius of the sphere (r) = 0.081029 m
[tex]T \infty[/tex] = 25 °C
[tex]T_i[/tex] = 124.978 °C
time (t) = 767.276 s
Using the formula :
[tex]\frac{T-T_{ \infty} }{T_i - T_{\infty}}= e^{-\frac{hA}{\rho V c_p}}*t[/tex]
where.
[tex]\frac{V}{A}= \frac{r}{3}[/tex]
Replacing our values ;we have:
[tex]\frac{T-25 }{124.978 - 25}= e^{-\frac{-103.067*3}{2700*897*0.081029}}*767.276[/tex]
[tex]\frac{T-25 }{124.978 - 25}= e^{{-0.001576}*767.276[/tex]
[tex]\frac{T-25 }{124.978 - 25}= e^{-1.209}[/tex]
[tex]\frac{T-25 }{99.978}= 0.2985[/tex]
[tex]{T-25 }= 0.2985*{99.978}[/tex]
[tex]{T-25 }= 29.843433[/tex]
[tex]{T= 29.843433+25 }[/tex]
[tex]{T= 54.843433[/tex]
T ≅ 54.84 ° C
Therefore, its surface temperature = 54.84 ° C
