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Anvisha [2.4K]
3 years ago
13

A sphere of radius 0.081029 m is made of aluminum. It is submerged in flowing water with a temperature of 25 °C that results in

a heat transfer coefficient of 103.067 W/m2•K. Its surface temperature is 124.978 °C at 0 s. What will its surface temperature be at 767.276 s? (Answer in °C.)
Physics
1 answer:
Dimas [21]3 years ago
6 0

Answer:

its surface temperature = 54.84 ° C

Explanation:

The density of aluminium (\rho) = 2700 kg/m ³

Heat capacity ( c_p) = 897 J/Kg.K

radius of the sphere (r) = 0.081029 m

T \infty = 25 °C

T_i = 124.978  °C

time (t) = 767.276 s

Using the formula :

\frac{T-T_{ \infty} }{T_i - T_{\infty}}= e^{-\frac{hA}{\rho V c_p}}*t

where.

\frac{V}{A}= \frac{r}{3}

Replacing our values ;we have:

\frac{T-25 }{124.978 - 25}= e^{-\frac{-103.067*3}{2700*897*0.081029}}*767.276

\frac{T-25 }{124.978 - 25}= e^{{-0.001576}*767.276

\frac{T-25 }{124.978 - 25}= e^{-1.209}

\frac{T-25 }{99.978}= 0.2985

{T-25 }= 0.2985*{99.978}

{T-25 }= 29.843433

{T= 29.843433+25 }

{T= 54.843433

T ≅ 54.84 ° C

Therefore, its surface temperature = 54.84 ° C

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