Question

A local barista serves coffee at 85°C. You add ice to the coffee to cool it to 55°C. Assume that an ice cube is 24 g and -18.5°C. How many ice cubes would you need to add to your 355 mL cup of coffee to bring it to 55°C? The specific heat of ice is 2.05 J/g°C, the specific heat of water is 4.184 J/g°C, and the specific heat of fusion of water is 334 J/g. Remember that an ice cube will need to be warmed to 0°C, will melt, and then the newly melted water will be warmed to 55°C.

A.2
B.4
C.3
D.1

Answer 1

The required number of ice cubes are "3".

Given:

Mass of coffee,

• 355 g

Specific heat of ice,

• 2.05 J/g°C

Specific heat of water,

• 4.184 J/g°C

Specific heat of water's fusion,

• 334 J/g

Let,

The required no. of ice cubes be "n".

→ Heat lost by coffee will be:

= $355\times 4.185\times 30$

= $44559.6 \ J$

→ Heat gained by no. of ice cubes will be:

= $24n\times 2.05\times 18.5$

= $910.2 \ n \ J$

→ Required heat by ice to melt will be:

= $24n\times 334$

= $8.016 \ n \ J$

→ Required heat by water will be:

= $24n\times 4.184\times 55$

= $5522.88 \ n \ J$

hence,

We know that,

→ $Heat \ lost \ by \ coffee = Total \ heat \ gained \ by \ ice \ cubes$

                      $44559.6 = 14449.08 \ n$

                                $n = \frac{44559.6}{14449.08}$

                                $n = 3$

Thus the above answer i.e., option C is the right answer.    

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Answer 2

Answer:

The required number of ice cubes are "3".

Explanation: