One end of a metal rod, which is insulated from the environment, has a length of

Question

One end of a metal rod, which is insulated from the environment, has a length of 0.30 m and cross-sectional area 2.00 x 10-5 m2, sits in a vessel of water boiling at 100 oC. The other end is immersed in a mixture of ice and water at 0 oC. The heat conducted along the rod melts 20.00 g of ice in 15.00 minutes.

a) Find the heat transported per second along the rod.
b) Calculate the thermal conductivity K of the material in the rod.

(Latent heat of fusion for ice is Lf = 333 x 103 J kg-1.)

can you please show the formula used in this question

Explanation / Answer

a)

P = Q/t = (m Lf)/t = (20e-3*333e3)/(15*60) = 7.4 W

b)

P = K A deltaT/L

==> K = L P/(A deltaT) = 0.30*7.4/(2e-5*100) = 1110

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