Ice absorbs total energy Q which from its environment to change from solid to liquid. Q is proportional to the heat of fusion h _f . If the mass of the ice is m: then Q = h _f m. For a closed system:
heat absorbed = heat given off. Thus:

h _f m + c _w m (T2 − 0) = c _w m _w (T1 − T2) + c _r m _r (T1 − T2) + q ………(1)
Where,

• m is the mass of ice
• m _w is the mass of water
• m _r is the mass of the reservoir and stirrer (assuming they are both made of the same material)
• c _w is the specific heat of water
• c _r is the specific heat of the (aluminum) reservoir
• q is the heat released by the thermometer which is equal to:
                                 q = 1.93V (T1 − T2) --------(2)
• V is the immersed volume of the thermometer in ml which can be determined by Archimedes’ Principle

Questions:
1) Derive an equation for the uncertainty in h _f from equation 1 above
2) Why is it only the immersed volume of the thermometer that matters in equation 2 above?