# How many kg of ice must be dropped to make Tf= 22.7C?

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1. Apr 10, 2016

1. The problem statement, all variables and given/known data
An insulated beaker with neglible mass contains .3kg of water at a temp of 78.6 C. How many kg of ice at -19.6 C must be dropped into the water to make Tf= 22.7C?
Specific heat for water= 4190 J/kgK
specific heat for ice= 2100 J/kgK
heat of fusion for water= 334kJ/kg

2. Relevant equations
Q=mc(Tf-Ti)
Q=mL

3. The attempt at a solution
Q1 = bring ice to 0 C
• Q=micec(Tf-Ti)
• Q=mice(2100 J/kgK)(0-19.6)
• Q= 41160mice
Q2 = melt ice (phase change)
• Q=mL
• Q=mice(334000 J/kg)
Q3= cool down water
• Q=mwaterc(Tf-Ti)
• Q=(.3kg)(4190 J/kgK)(22.7 - 78.6)
• Q=-70266.9 J
Q1+Q2+Q3=0
41160mice + 334000mice + (-70266.9)=0
375160mice= 70266.9
mice = .187kg

This answer isn't correct. What did I do wrong or what did I miss? I'm thinking maybe I missed another Q but I don't know what it could be.

2. Apr 10, 2016

### SteamKing

Staff Emeritus
Remember, once the ice melts, the liquid from this mixes with the liquid already in the beaker.

The final temperature of 22.7 °C must be reached by all of the liquid in the beaker.

3. Apr 10, 2016

Then would Q3 have to include both the masses?

4. Apr 10, 2016

### SteamKing

Staff Emeritus
Yep. You can't separate the melt water from the warm water already in the beaker when the ice was dropped in.

5. Apr 10, 2016

So then its
Q3=(mice+mwater)c(Tf-Ti)
=(.3kg + mice)(4190)(22.7-78.6)
=(.3kg + mice)(-234221)
= -70266.3 - 234221mice

And then add this Q3 to the others and set =0?

6. Apr 10, 2016

### SteamKing

Staff Emeritus
Be careful here.

The warm water in the beaker is being cooled from 78.6 °C to 22.7 °C.
The melt water is being warmed from 0 °C to 22.7 °C.

Your equations should reflect this.

7. Apr 10, 2016

So what I really need is 2 extra equations then?

8. Apr 10, 2016

No, nevermind. Just one. For the ice water. Q4= micecice(22.7-0)

9. Apr 10, 2016

### SteamKing

Staff Emeritus
Remember, the ice has already melted. cice should be cwater.

10. Apr 10, 2016