# physics

posted by .

Your 300mL cup of coffee is too hot to drink when served at 87C. What is the mass of an ice cube, taken from a -20C freezer, that will cool your coffee to a pleasant 58C?

• physics -

You want to remove M C (delta T) = 300 g*1.00 Cal/(g C) * 29 C = 8700 calories from the coffee. If m is the mass of ice you add, the heat absorbed by the ice while melting and incresing in temperature from -20 to +58 C is
m*Cice*(20) + mCwater*58 + m*80 Cal/g

The specific heat of ice, Cice = 0.51 Cal/g C

8700 cal = 10.2 m + 58 m + 80 m = 148.2
Solve for m

• physics -

q1 = heat to move ice from -20 to zero.
q1 = mass ice x specific heat ice x (Tfinal-Tinitial). [Tf will be 0 and Ti will be -20 but watch that sign since it will change.

q2 = heat to melt the ice.
q2 = mass ice x heat fusion.

q3 = heat to move ice from zero to 58.
q3 = mass ice x specific heat water (its now a liquid) x (58-0).

q4 = loss of heat to move 300 mL water from 87 to 58.
q4 = mass water x specific heat water x (58-87).
q1 + q2 + q3 + q4 = 0
You have only one unknown in all of the above which is mass ice. Solve for that. Check my thinking. I won't be on for the next 6 hours or so.

## Similar Questions

1. ### Physics

5) An insulated Thermos contains 190 cm3 of hot coffee at 79.0°C. You put in a 11.0 g ice cube at its melting point to cool the coffee. By how many degrees (in Celsius) has your coffee cooled once the ice has melted and equilibrium …
2. ### Science

Suppose in a restaurant your coffee is served about 5 or 10 minutes before you are ready for it. If you want the coffee to be as hot as possible when you drink it, should you pour in the room temperature cream right away or when you …
3. ### MATH MIDDLE SCHOOL

I love chocolate and coffee. I begin by making one cup of hot chocolate. I drink half of my cup and then I fill the cup with coffee. I stir the new mixture and drink half of the cup and then fill the cup again with coffee. I continue …
4. ### Math Middle School

Please help me solve this challenge problem: I love hot chocolate and coffee. I began by making one cup of hot chocolate. I drink half of my cup and then I fill the cup with coffee. I stir the new mixture and drink half of the cup …
5. ### physics

An insulated Thermos contains 140 cm3 of hot coffee at 89.0°C. You put in a 11.0 g ice cube at its melting point to cool the coffee. By how many degrees (in Celsius) has your coffee cooled once the ice has melted and equilibrium is …
6. ### physics

An insulated Thermos contains 140 cm3 of hot coffee at 89.0°C. You put in a 11.0 g ice cube at its melting point to cool the coffee. By how many degrees (in Celsius) has your coffee cooled once the ice has melted and equilibrium is …
7. ### Chemistry/Calorimetry

You buy coffee (200.0 ml) served in a styrofoam cup. You are up late working in a chemistry lab, and want to drink the coffee right away, but at 95.0 degrees C, it is too hot to drink. You like the temperature of your coffee to be …
8. ### Chemistry

At a local convenience store, you purchase a cup of coffee, but, at 98.4oC, it is too hot to drink. You add 23.0 g of ice that is –2.2oC to 248 mL of the coffee. What is the final temperature of the coffee?
9. ### physics

The "steam" above a freshly made cup of instant coffee is really water vapor droplets condensing after evaporating from the hot coffee. What is the final temperature of 200 g of hot coffee initially at 90.0°C if 2.00 g evaporates …
10. ### physics

The "steam" above a freshly made cup of instant coffee is really water vapor droplets condensing after evaporating from the hot coffee. What is the final temperature of 280 g of hot coffee initially at 90.0°C if 2.50 g evaporates …

More Similar Questions