# Heat and work

From what height one would have to drop a block of ice so that the energy obtained would be enough to melt the block and raise the temp of the water to 50 C.

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

To melt the block and raise the temp of water to 50 C we need to supply latent heat to melt the block and then to raise it from a temperature of 0 degrees Celsius to 50 degrees celsius

We assume that the block of ice is at a temperature of 0 degrees Celsius

Let the mass of the block be m Kg

The specific latent heat of fusion of ice at 0 ÂºC, is 334 kJ.kg-1. This means that to convert 1 kg of ice at 0 ÂºC to 1 kg of water at 0 ÂºC, 334 kJ of heat must be absorbed by the ice.

Therefore the latent heat required is 334 * m kJ

The specific heat capacity of water is 4.18 kJ.kg-1.K-1.

Specific heat capacity is the quantity of heat required to raise the temperature of a unit of mass of a substance by a unit change in temperature.

Thus to raise the temperature of water from 0 degrees Celsius to 50 degrees Celsius i.e. a change of 50 degrees Celsius the amount of heat required is m x 4.18 x 50 kJ = 209 m kJ

Thus the total heat required is equal to (334 m + 209 m) kJ or (543 x 1000 ) m Joules

This heat is to be supplied by the loss in Potential energy as the block falls for a distance of h meters

Loss of Potential Energy = m g h

where g= acceleration due to gravity = 9.81 m /s^2

Equating the two

mgh = (543 x 1000 ) m

We can cancel m from both sides of the equation

thus

gh= 543 x 1000

or h = 543 x 1000 / 9.81= 55352 m or 55.352 Km

Answer: 55352 m or 55.352 Km

Â© BrainMass Inc. brainmass.com December 24, 2021, 5:11 pm ad1c9bdddf>https://brainmass.com/physics/work/heat-work-34092