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frutty [35]
3 years ago
9

A 4 cm diameter sphere of copper is initially at a temperature of 95 °C. It is placed in a very large water bath at time t- 0. T

he water bath is initially at a uniform temperature of 25 °C. The heat transfer coefficient is estimated to be 400 watts / (m2 °C). The specific heat of copper is 0.385 Joule (gram °C) and its density is approximately 9 gram per cc. Estimate the time at which the average temperature of the sphere will be 35 °C.
Engineering
1 answer:
avanturin [10]3 years ago
4 0

Answer:112.376 s

Explanation:

Given

T_i=95^{\circ}C

T_f=35^{\circ}C

T_\infty \left ( ambient\right )=25^{\circ}C

h=400 watts/\left ( m^{2}^{\circ}C\right )

c=0.385 J/\left ( m^2^{\circ}C\right )

\rho =9 gm/cm^{3}

Using Newton's law of cooling

\frac{T_i-T_{\infty}}{T-T_{\infty}}=e^{\frac{ht}{\rho L_{c}c}}

\frac{95-25}{35-25}=e^{\frac{400\times 3\times 10^{-4}\times t}{9\times 2\times 0.385}}

7=e^{1.7316\times 10^{-2}\times t}

Taking log both side

t=112.376sec

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