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Question

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?

Answer 1

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

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Answer 2

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

Comments

Where
c = specific latent heat
m = mass of the ice