Experiment 9: Specific Heat Capacity and Calorimetry — Worked Examples

A $0.0800\,\text{kg}$ metal sample at $95.0^\circ\text{C}$ is placed in $0.150\,\text{kg}$ of water initially at $24.0^\circ\text{C}$. The equilibrium temperature is $31.0^\circ\text{C}$. Neglect calorimeter heat capacity and use $c_w=4184\,\text{J/(kg·K)}$. Determine the sample specific heat.

Use the same data as Example 1, but the calorimeter heat capacity is $C_{cal}=35\,\text{J/K}$. Determine the corrected specific heat.

If the reference specific heat for the aluminum sample is $900\,\text{J/(kg·K)}$, determine the percent error of the corrected result $906\,\text{J/(kg·K)}$.

A calorimeter initially contains $0.150\,\text{kg}$ of water at $22.0^\circ\text{C}$. It receives $0.100\,\text{kg}$ of warm water at $60.0^\circ\text{C}$. The final temperature is $36.7^\circ\text{C}$. Determine $C_{cal}$.

For $m_s=0.0800\,\text{kg}$, $m_w=0.150\,\text{kg}$, $C_{cal}=35\,\text{J/K}$, $T_{w,i}=24.0^\circ\text{C}$, and $T_f=31.0^\circ\text{C}$, compare the calculated $c_s$ if the sample actually enters at $90.0^\circ\text{C}$ but the experimenter incorrectly substitutes the $95.0^\circ\text{C}$ bath temperature.

A wet sample carries $2.0\,\text{g}$ of $95^\circ\text{C}$ bath water into a calorimeter that reaches $31^\circ\text{C}$. Estimate the energy released by that unaccounted water.

A $0.050\,\text{kg}$ copper sample with $c=385\,\text{J/(kg·K)}$ at $90.0^\circ\text{C}$ is placed in $0.100\,\text{kg}$ of water at $25.0^\circ\text{C}$. Neglect the calorimeter. Predict the equilibrium temperature.

Using the corrected setup from Example 2, calculate $c_s$ if the accepted final temperature were $30.8^\circ\text{C}$ and $31.2^\circ\text{C}$ instead of $31.0^\circ\text{C}$.