A certain pond absorbs I = 775 W/m2 for a time period of an hour from the sun. Assume that all of this energy is used to raise the temperature of the pond. The pond water fills a hemisphere of radius r = 2.75 m and has a density = 1000 kg/m3. The specific heat of the pond water is c = 4186 J/(kgK).

(a) What is the change in temperature T in kelvins of the pond due to this energy transfer?

(b) What is the change in the internal energy of the pond U in joules, assuming that it does no work and loses no energy as heat?

(c) If the initial temperature of the pond was T = 20.0C, what would be the change in the entropy S of the pond, in joules per kelvin?

(d) If the pond were at a temperature of T = 0.0C and covered by a d = 0.10 m thick layer of ice at this same temperature, how long t in hours would it take to melt the ice? The latent heat of fusion for ice is L_f = 334 kJ/kg and its density is _ice = 917 kg/m³. Assume that the layer of ice has the form of a cylinder of thickness d and cross-sectional radius r.

(e)

If the thickness of the ice were doubled, would it take twice as long to melt the ice?

There is not enough information.

Because the time it takes to melt the ice is linearly dependent ond, it would take twice as long to melt the ice if the thickness were doubled.

Because the time it takes to melt the ice is linearly dependent ond, it would not take twice as long to melt the ice if the thickness were doubled.

The time it takes to melt the ice is independent ofd.

Because the time it takes to melt the ice is inversely dependent ond, it would take half as long to melt the ice if the thickness were doubled.

Because the time it takes to melt the ice is inversely dependent ond, it would take twice as long to melt the ice if the thickness were doubled.

(f)

If the radius of the pond were doubled, would it take longer to melt the ice?

There is not enough information.

The time it takes to melt the ice is independent ofr.

Yes, because the time it takes to melt the ice is linearly dependent onr, it would take longer to melt the ice ifrwere doubled.

Yes, because the time it takes to melt the ice is inversely dependent onr, it would take longer to melt the ice ifrwere doubled.

Yes, because the time it takes to melt the ice is linearly dependent onr, it would take longer to melt the ice ifrwere doubled.

Yes, because the time it takes to melt the ice is inversely dependent onr, it would take longer to melt the ice ifrwere doubled.