Question

You have 100 g of H2O(l) at 55 ̊C that you cool by adding 10 g...

You have 100 g of H2O(l) at 55 ̊C that you cool by adding 10 g of ice from a -10 ̊C freezer. The system is open to a constant pressure environment and is in an adiabatically-insulating styrofoam cup. Calculate the final temperature of the system.

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Answer #1

specific heat capicty of ice = 2.1J/g.oC
heat requiresd to change the temperature of ice from -10 oC to 0 oC
= m*(specific heat capicty of ice)*(T2-T1)
= 10*2.1*(0+10)
= 210 J

latent heat of fusion of ice = 334 J/oC
heat required to melt all ice
= m*(latent heat of fusion of ice)
= 10*334
= 3340 J

now let final temperature be T
use,
heat requiresd to change the temperature of ice from -10 oC to 0 oC+heat required to melt all ice +mICE*s*(T-0) = mWATER*s*(55-T)
s = specific heat capicty of water
= 4.18 J/g.oC
so,
210+3340+10*4.18*T = 100*4.18*(55-T)
3550 + 41.8T = 22990 - 418T
459.8T = 19440
T = 42.28 oC

Answer : 42.28 oC

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