Chapter 14, Problem 33P

A cube of ice is taken from the freezer at -8.5°C and placed in an 85-g aluminum calorimeter filled with 310 g of water at room temperature of 20.0°C. The final situation is all water at 17.0°C. What was the mass of the ice cube?

To determine

Mass of ice cube

Answer to Problem 33P

Solution:

$\text{9}.\text{77 g}$

Explanation of Solution

Given Info:

Initial temperature is -8.5°C and placed in 85 g aluminum calorimeter with 310g of water at room temperature of 20°C. Final temperature is 17°C.

Formula used:

Heat for melting is given by

$Q=mL$

Where L is latent heat

$Q=mc\Delta T$

Calculation:

Heat lost by water and aluminum at room temperature can be calculated as

$\begin{array}{l}Q=m_w{c}_w\Delta T+m_a{c}_a\Delta T\\ Q=0.310kg\times 4186J/kg°C\times (20-17)°C+0.085kg\times 900J/kg°C\times (20-17)°C\\ Q=4122.5J\end{array}$

The heat required for raising the temperature of ice melts the ice and increases the temperature to 17°C

$\begin{array}{l}m=\frac{Q}{c_i\Delta T_i+L+c_m\Delta T_w}\\ m=\frac{4122.5J}{2100\text{J/kg°C}\times 8.5°C+3.35\times {10}^5\text{J/kg}+4186\text{J/kg°C}\times 17.0\text{J/kg}}\\ m=0.00977\text{kg}=9.77\text{g}\end{array}$