/sci/ - Science & Math

>>2382525

hi there /sci/ i have a problem, i am told several variables and using them i am supposed to prove the latent heat of fusion.

what i am given is the mass of water + its initial temperature (0.2955 KG + 54 degrees Celsius)

a block of ice measuring 0.0064 KG at a temperature of 0 degrees Celsius is then added (it begins to melt instantly)
the final temperature of the water is 52 degrees Celsius.

i figured what to do is to find out the heat lost by the water since heat lost=heat gained
heat lost is Eh=M.C.DT
>M= mass
>c=heat capacity
>DT= change in temperature
>^C = degrees Celsius
this works out to 2415J (0.2955KG*4200J/KG^C *2^C)
now that i have the heat lost the heat gained should be 2415J=M*latent heat of fusion (water) + heat gained by melted ice.

heat gained by melted ice worked out to 1397.76J (0.0064KG* 4200J/KG^C * 52^C)

this gives me 2415J=0.0064KG*latent heat of fusion +1397.76J

what do i do now? i know that the correct answer is 3.3*10^3 J/KG or 330000 J/KG but i need to show HOW i got there