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Question 3: A lead bar is placed on a block of ice that is much larger (in

surface area) than the bar. The entire system is kept at 0 °C. As a result of the

pressure exerted by the bar, the ice melts beneath the bar and refreezes above

the bar. Thus, heat is released above the bar, conducted through the metal, and

then absorbed by the ice below the bar. Find an approximate expression for the

speed at which the bar sinks through the ice. Your answer should be in terms

of the latent heat of fusion L per kilogram of ice, the densities Pice and pwater

of ice and water, respectively, the thermal conductivity of lead, the absolute

temperature T, the acceleration due to gravity g, and the density of lead Plead

A little guidance: Probably the best way to solve this problem is to com-

bine our friend the Clausius-Claperyon equation with the equation that defines

thermal conductivity: = KA, where A is the cross-sectional area of the

bar and h is the height (or thickness) of the bar.

Fig: 1