A solid metallic sphere of diameter 20 cm and mass 10 kg is heated to a temperature of `327^@C` and suspended in a box in which a constant temperature of `27^@C` is maintained. Find the rate at which the temperature of the Sphere will fall with time. Stefan's constant`=5.67xx10^-8W//m^(2)//K^(4)` and specific heat of metal `=420J//kg//^(@)C`.

Options

A. `0.055^@C//s`
B. `0.066^@C//s`
C. `0.044^@C//s`
D. `0.03^@C//s`

Answer

B

Explanation

Rate of heat loss`=sigmaeA(T^4-T_S^4)`
`-ms(dT)/(dt)=sigmaeA(T^4-T_S^4)`
`-(dT)/(dt)=(5.8xx10^-4xx1xxpi(0.08)^2[(500)^4-(300)^4])/(10xx4.2xx90)`
`(-dT)/(dt)=0.066^@ C//s`