# How does ice affect a drink?

1. Dec 16, 2015

### Kbenjamin827

1. The problem statement, all variables and given/known data
we have 42 grams of rum with a specific heat of 1.7 and 113 grams of coke with a specific heat of .85 and both liquids are room temperature (25 degrees Celsius). when you add 85 grams of ice (-10 degrees Celsius) into this mix, what will the final temperature be and how long will it take to reach that temperature?

2. Relevant equations
mC(temperature), where m is mass in grams and C is the specific heat.

3. The attempt at a solution
mC(temp of ice) + m(latent) + mC(temperature of melted ice) = mC(temp of rum) + mC(temp of coke)

2. Dec 16, 2015

### Staff: Mentor

You haven't evolved your attempt much. What is your strategy? What have you tried? We need to see more of your efforts.

3. Dec 16, 2015

### Staff: Mentor

Is this a real homework problem, including how long it takes to reach the final temperature? Also, do you feel that all the ice is going to melt?

You have written an equation down, but I don't see any answer. Let's see some numbers.

Chet

4. Dec 16, 2015

### SteamKing

Staff Emeritus
Specific heat values have units. What are the units of 1.7 and 0.85?

5. Dec 16, 2015

### Kbenjamin827

Cal/gram

6. Dec 16, 2015

### Kbenjamin827

I did heat gained = heat lost

7. Dec 16, 2015

### Kbenjamin827

I got approximately -2.08 degrees, so I guess the ice doesn't fully melt

8. Dec 16, 2015

### Staff: Mentor

We are here to help, but we won't do your homework for you.

Otherwise the thread will be closed.

9. Dec 16, 2015

### Kbenjamin827

10. Dec 16, 2015

### Kbenjamin827

Just realized I made a mistake in my calculations in my picture, it is -11 not -2 :/

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11. Dec 16, 2015

### Staff: Mentor

This is a problem where you can't write a single equation to solve for the final state. Since at least one of the substances involved (the water ice) has the potential for a state change (melting) you need to proceed in stages and make some decisions along the way as to what specific heats or heats of fusion are involved. Since the "bump in the road" is the melting of ice, check the quantities of heat involved in getting the materials from their initial temperatures to the transition temperature (0C).

Start by calculating how much heat would be required to raise the ice temperature to the freezing point without melting it and how much heat would need to be extracted from the fluids (in total) to bring them to the same temperature (0C).

What do you find? How do they compare? Can you plan a next step based on these values?

12. Dec 16, 2015

### Kbenjamin827

I calculated how much it would take to go from -10 to 0, which is about 450, and to melt it would be about 26000. The Coke and run out out about 4000, so it's enough to bring it to 0 but not to melt the ice. I'm not sure how to find the time it takes for the environment to melt the ice. I figured I'd find the final temperature of everything mixed together before I find how it takes for the rum Coke and now water to get to 25 degrees.

13. Dec 17, 2015

### Staff: Mentor

Can you show your calculations? Be sure to include units for everything. Your value for the heat required to bring the ice from -10C to 0C, "about 450", for example means nothing without units. What specific heat value are you using for ice? State all your specific heat values with units.