# Latent Heat Of Fusion

Homework Helper

## Homework Statement

How much heat is required to heat 0.2kg of ice from -20°C to 30°C?

## Homework Equations

Total heat lost or gained : ##Q = mcΔt## where ##Δt## is the change in temperature and c is the heat capacity.

Latent Heat Fusion : ##Q = mL_f##

## The Attempt at a Solution

From my understanding, I think I need to break this problem down into states.

The ice will start melting at 0°C ( since ice is just condensed water ). So the ice must be heated from -20°C to 0°C for it to melt.

Then we must use Latent Heat to melt the ice.

Finally we would have to heat the water from 0°C to 30°C.

So the amount of heat we would need can be expressed by the equation :

##Q_T = Q_{Ice} + Q_{Melt} + Q_{Water} = mc_{Ice}Δt_{Ice} + mL_f + mc_{Water}Δt_{Water}##

Then plugging and chugging I get :

##(0.2 kg)(2100 J/kg°C)(0°C + 20°C) + (0.2 kg)(330000 J/kg) + (0.2)(4200 J/kg°C)(30°C - 0°C) = 99600J##

Therefore 99600J of heat would be required to heat the ice from its original state to a heated state of water.

Does this look okay?

TSny
Homework Helper
Gold Member
Looks good!

Doc Al
Mentor
Yep, looks good to me as well.

BruceW
Homework Helper
yep. looks good to me too. Although you have used 2 significant figures in your values, so does it make sense to have 3 significant figures in your answer?

edit: hehe, everyone seems to have posted a reply near-simultaneously.

Homework Helper
BruceW said:
edit: hehe, everyone seems to have posted a reply near-simultaneously.

You're all so fast lol. Thanks for the confirm guys :).

"edit: hehe, everyone seems to have posted a reply near-simultaneously. " It's because it was an easy problem :-)