# 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:

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

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

###### 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.