Heat and Conservation of Energy

[bfite8]

Homework Statement

A large punch bowl holds 3.00 kg of lemonade (which is essentially just water) at 1.00 degree celsius. A 0.055 kg ice cube at 0 degrees is placed in the lemonade. What is the final temperature of the system?

Homework Equations

Q=mcΔT
Q=mL

The Attempt at a Solution

Having a hard time understanding the concept of heat lost and gained and when to use the latent heat equation in problems.
All I really know of how to start this out is Q(water) + Q(ice)=0

 

[Borek]

Lemonade cools down, ice melts. Question is, is there enough ice to cool the lemonade to zero?

 

[bfite8]

i have no clue tbh

 

[Borek]

I was trying to point you in the right direction, you took my comment too literally. Whether there is enough ice is a thing that has to be calculated.

How much heat is needed to melt the ice?

How much heat would you get from the water cooling it down to 0°C?

 

[bfite8]

I was trying to point you in the right direction, you took my comment too literally. Whether there is enough ice is a thing that has to be calculated.

How much heat is needed to melt the ice?

How much heat would you get from the water cooling it down to 0°C?

ok so for this i need to use (mass of ice)(latent heat of fusion)and (mass of water)(latent heat of fusion) ?

i think this is somewhat on the right track. thank you sir for helping

 

[Borek]

Melting the ice is a process described by the latent heat equation.

Cooling down the water is a process described by the other equation, the one with ΔT.

 

[bfite8]

ah right thanks. don't know why i thought of using the latent heat equation for the water. it's just cooling down, not changing phase