Two cooking pots are identical in every respect except that one has a 0.64 cm th

Question

Two cooking pots are identical in every respect except that one has a 0.64 cm thick copper bottom and the other has an aluminium bottom. How thick should the aluminium bottom be in order for it to conduct the same amount of heat from a stove burner in the same time as the copper bottom? The thermal conductivity of copper is 390 J/(s m C degree) and that of aluminium is 240 J/(s m C degree). A star radiates as if it were a blackbody with a temperature of 3000 K. If it radiates the same power as the sun, what is the ratio of its radius to the radius of the sun? Assume the sun has a blackbody temperature of 6000 K. The surface area of a sphere is given by 4 pi R^2.

Explanation / Answer

7. Rate of heat conduction,

Q/t = k A dT/dx

A(cross section area ) and dT ( temp difference between two surfaces)

are same for both .

hennce k / L = constant

390 / 0.64 = 240 / d

d = 0.394 cm thick

8. Power radiated = sigma T^4 area

sigma is universal constant .

3000^4 ( 4 pi Rr^2) = 6000^4 ( 4 pi Rs^2)

Rr / Rs = (6000 / 3000)^2 = 4

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