Question

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. The 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.

Answer 1

Answer:112.376 s

Step-by-step 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

`(T_i-T_(\infty))/(T-T_(\infty))`=
`e^{(ht)/(\rho L_(c)c)}`

`(95-25)/(35-25)`=
`e^{(400* 3* 10^(-4)* t)/(9* 2* 0.385)}`

7=
`e^{1.7316* 10^(-2)* t}`

Taking log both side

t=112.376sec