# How do I find the latent heat of fusion of frozen sugar water?

OK, so basically I need to find the latent heat of fusion of my frozen sugar water for my experiment, but I don't think I can use the normal styrofoam cup with water. Because when some of the sugar water melts, it will mix with the water, so I can't really measure the energy absorbed by the water since it's not totally water anymore. Does anyone have a better method? I've tried looking on google, but they all show methods for regular ice and not ice with impurities inside. Thanks in advance.

Edit: my question was originally about specific heat capacity, but i realised it was supposed to be latent heat of fusion

• Can you edit your question to describe the "normal method" which you think will not work?
– rob
Oct 4, 2020 at 16:55
• basically u put a known amount of water in a styrofoam cup, n measure the temperature, then u add a known amount of ice n stir n wait until all the ice melts, then u record the final temperature. Then since the specific heat capacity of water is already known, u can then calculate the one for the ice Oct 4, 2020 at 18:28

The first step is finding the specific heat capacity of that sugar water solution. You cannot use ice cubes for this because as the ice melts, the concentration of the solution will change. So what you should do is take a hot piece of metal with a known specific heat ,like copper for example, at a temperature $$T_{hot}$$ and put it into the sugar water solution in the styrofoam cup at room temperature $$T_{room}$$. There are many ways of doing this but I would suggest pulling the metal from water that has been boiling at 373K for a reasonable amount of time so that $$T_{hot} = 373K$$. After putting the hot metal in the sugar water solution, monitor it's temperature until equilibrium is reached at say $$T_{final}$$. Then just use the fact that net heat change is (neglecting heat loss to surrounding) zero so that you have $$m_{w}c'(T_{final} - T_{room}) + m_{metal}c_{metal} (T_{final} - T_{hot}) = 0$$ If you measure $$m_w$$ and $$m_{metal}$$, then the only unknown is the specific heat capacity of the sugar water solution $$c'$$.
Finally, if you do not have any pure sample of metal with known specific heat, then take any piece of metal lying around and do the first experiment but this time with pure water so that the unknown to be found is $$c_{metal}$$.