I am having trouble with a Physics homework problem?

How much energy will it take to melt a block of ice of mass 15kg? If this same energy was used to lift the ice, to what height (in meters) could it be raised?

asked Jan 12, 2013 in PHYSICS

Q = mL
L is specific latent heat of melting.
L of water is 336000 J/kg
Therefore,
Q = 15 * 336000
Q = 5040000 J

Given that

The total energy required to melt 15 kg of ice

We know that ,

The energy required to melt is 334 kJ/kg

And Energy E= mc -------------> (1)

Here m = 15kg and c = 334 kJ/kg

E = 15kg*334kJ/kg

But , now the total energy required to melt the ice you can use the equation for potential energy

E = mgh -------------------(2)

Here 'm' is the mass of the ice is 15kg

'g' is the gravitational constant is 9.8 m²

and 'h' (often written dh or delta h) is the distance it will be raised

Now  (1) = (2)

There fore

mc = mgh

Divide each side by 'm'

mc / m = mgh / m

Simplify

c = gh

Divide each side by 'g'

c / g = (gh) / g

Simplify

c / g = h

h = c / g

Here c = 334 , g = 9.8m²

h = 334 / 9.8

Simplify

= 34.081m

height could it be raised is h = 34.081m