Calculate the mass of ice with heat transfer / latent heat

[adam640]

Homework Statement

Find m_i, the initial mass of ice.

T_i = -20
c_i = 2093Jkg^-1K^-1
T_s = +35
m_s = 2kg
c_s = 837.4Jkg^-1K^-1
c_w = 4187Jkg^-1K^-1
l_f = 3.35x10⁵Jkg_-1

S = solid
W = water
I = ice
l_f = latent heat of fusion of ice / water

Homework Equations

Q=mc\DeltaT
Q=C\DeltaT
Q=ml

The Attempt at a Solution

For the Solid
Q_s = (2)(837.4)(10-35)
Q_s = -4.187x10⁴J

For the Water / Ice
Q_i = m_ix(4.186x10⁴)
Q = m_ix(3.35x10⁵)
Q_w = m_ix(4.187x10⁴)

I don't know where to go from here, I have seen the markscheme however and I am aware that the answer is: m_i = 0.100kg

 

[gneill]

You've specified everything but the experimental circumstances. What are the initial and final conditions? Do you want to calculate the mass of ice remaining, or the initial mass of ice?

 

[adam640]

Oops, the Solid is placed on top of the ice. The ice then melts and the final temperature of both the solid and the ice is 10. So basically I'm looking for the initial mass of the ice, before the rock was placed onto it.

 

[gneill]

So, the final temperature is 10C. What does that tell you about the the water in the system?