Energy and Entropy 2024
This question is about the ice calorimeter lab we did in class
Plot your data
Plot the temperature of the system at time \(t\), with respect to the total energy that had been thermally added to the system at time \(t\). This thermally-added energy is called "heat". In this experiment, heat \(Q\) is increasing as a function of time. To find the net heat transferred from 0 to \(t\), you will need to integrate the power from 0 to \(t\). Discuss your \(T(Q)\) curve and any interesting features you notice on it.
Specific heat capacity From your data, find \(C_p\), the heat capacity of the liquid water in your cup at a particular temperature, and \(c_p\), the specific heat capacity of liquid water at a particular temperature. You can find the heat capacity by examing the slope of your \(T\) vs. \(Q\) graph. i.e.
\begin{align}
C_p = \frac{\text{Heat that entered the system during the temperature change}}{\Delta T}
\end{align}
where \(\Delta T\) is the temperature change. The S.I. units of heat capacity are joule/kelvin. The \(p\) subscript means that your measurement was made at constant pressure.How does your answer compare with the prediction of the Dulong-Petit law?
Latent heat of fusion
Looking at data from a group that vigorously stirred the ice bath, what did the temperature do while the ice was melting? How much energy was required to melt the ice in the calorimeter? How much energy was required per unit mass? per molecule?
Experimental uncertainty Compare your experimental values for \(c_p\) and latent heat to published values for water. If your values are larger or smaller, discuss systematic errors in the experiment that might be responsible. What would you do differently in a follow-up experiment?
Entropy of fusion The change in entropy is easy to measure for a reversible isothermal process (such as the slow melting of ice). It is
\begin{align}
\Delta S &= \frac{Q}{T}
\end{align}
where \(Q\) is the energy thermally added to complete the melting, and \(T\) is the temperature in kelvin. What is was change in the entropy of
the ice you melted? What was the change in entropy per
molecule? What was the change in entropy per molecule divided
by Boltzmann's constant?
Entropy for a temperature change Choose two temperatures that your water reached after the ice melted. Choose a reasonably large change in temperature (for example, from 2 C to 5 C). Use your experimental data to calculate the change in entropy of the water between these two temperatures. Hint: this change is given by
\begin{align}
\Delta S &= \int \frac{{\mathit{\unicode{273}}} Q}{T} \\
&= \int \frac{P(t)}{T(t)}dt
\end{align}
where \(P(t)\) is the heater power as a function of time and \(T(t)\) is
the temperature as a function of time, and the limits of integration are the final and inital times. Do this integral numerically, using your raw data (discrete time points).