How much ice is required to cool a 10.0oz drink from 73°F to 33°F, if the heat capacity of the drink is 4.18 J/g°C?

Question

Express answer using two significant figures 

 

Also, assume that the heat transfer is 100 % efficient.

Answer 1

It depends what the temperature of the ice is and whether it is cold enough to avoid melting in the drink.

 

If it is cold enough, then you need to calculate the amount of heat that the drink has to give up to cool from 73°F to 33°F, and then calculate how much ice is needed to absorb that much heat.

 

But if the ice is going to melt, there is a whole different solution, and it completely depends on what the starting temperature of the ice is.

 

The ice will absorb heat from the drink to raise its temperature to 32 °F.  The specific heat of the ice is 2.11 J / g °C.

 

Then the ice will melt.  This will absorb more heat without changing the temperature of the resulting liquid water.  The heat of fusion of water/ice is 334 J / g.

 

Then you will have some amount of water at 32 °F which will continue to cool the drink down to 33 °F.  The specific heat of the cold water is the same as the drink, 4.18 J/g °C.

 

So without knowing the starting temperature of the ice, we really can't figure this out.