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A solid metallic sphere of diameter 20 c...

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`.

Text Solution

Verified by Experts

The rate of loss of heat by the sphere is given by
`(dQ)/(dt) = sigmaA(T^(4)-T_(0)^(4))`
Wliere A is the surface area of the sphere = `4pir^(2), with r =10cm=0.1 m, T= 327^(@)C = 600K and T_(0) = 27^(@)C = 300K`.
Thus `(dQ)/(dt) = 5.67 xx 10^(-8) xx 4 pi xx (0.1)^(2) xx {(600)^(4) -(300)^(4)}`
`=866 Js^(-1)`
Now dQ = msdT, where dT is the fall in temperature in time dt.
`(dQ)/(dt) = ms (dT)/(dt)`
or `866 = 10 xx 420 xx (dT)/(dt)`
or `(dT)/(dt) =(866)/(4200) = 0.206^(@)C//s`
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Knowledge Check

  • A metallic sphere having radius 0.08 m and mass m = 10 kg is heated to a temperature of 227^(@)C and suspended inside a box whose walls ae at a temperature of 27^(@)C . The maximum rate at which its temperature will fall is:- (Take e =1 , Stefan's constant sigma = 5.8 xx 10^(-8) W//m^(-2)K^(-4) and specific heat of the metal s = 90 cal//kg//deg J = 4.2 "Joules"//"Calorie")

    A
    `0.55^(@)C//sec`
    B
    `0.66^(@)C//sec`
    C
    `0.44^(@)C//sec`
    D
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  • A metallic sphere having radius 0.08 m and mass m = 10kg is heated to a temperature of 227^(@)C and suspended inside a box whose walls are at a temperature of 27^(@)C . The maximum rate at which its temperature will fall is :- (Take e = 1, Stefan's constant sigma=5.8xx10^(-5)Wm^(-2)K^(-4) and specific heat of the metal s = 90 cal/kg/deg J = 4.2 Joules/Calorie)

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    `.055""^(@)C//sec`
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  • A body having a surface area of 50cm^2 radiates 300J of energy per minute at a temperature of 727^(@)C . The emissivity of the body is ( Stefan's constant =5.67xx10^(-8)W//m^2K^4 )

    A
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    B
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    C
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    D
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