# Problem: An ice cube of mass 9.0 g at temperature 0oC is added to a cup of coffee, whose temperature is 95 oC and which contains 130 g of liquid. Assume the specific heat capacity of the coffee is the same as that of water. The heat of fusion of ice (the heat associated with ice melting) is 6.0 kJ/mol.Find the temperature of the coffee after the ice melts. Express your answer using two significant figures.

###### FREE Expert Solution

$\mathbf{q}\mathbf{=}\mathbf{mc}\mathbf{∆}\mathbf{T}$

• (+) → gains heat
• (-) → loses heat

-qcoffee = +qice

When ice melts at 0°C:

$\overline{){\mathbf{q}}{\mathbf{=}}{\mathbf{n}}{\mathbf{×}}{{\mathbf{\Delta H}}}_{{\mathbf{fusion}}}}\phantom{\rule{0ex}{0ex}}$

${\mathbf{q}}_{\mathbf{ice}}\mathbf{=}\mathbf{mc}\mathbf{∆}\mathbf{T}\mathbf{+}\mathbf{n}\mathbf{∆}{\mathbf{H}}_{\mathbf{fusion}}$

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###### Problem Details

An ice cube of mass 9.0 g at temperature 0oC is added to a cup of coffee, whose temperature is 95 oC and which contains 130 g of liquid. Assume the specific heat capacity of the coffee is the same as that of water. The heat of fusion of ice (the heat associated with ice melting) is 6.0 kJ/mol.

Find the temperature of the coffee after the ice melts. Express your answer using two significant figures.

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Heating and Cooling Curves concept. You can view video lessons to learn Heating and Cooling Curves. Or if you need more Heating and Cooling Curves practice, you can also practice Heating and Cooling Curves practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Acharya's class at RICHLAND.