Exercises: Entropy and spontaneity

Topic challenge. Is your kitchen efficient? Evaluate the thermodynamics of heating water in your home in the context of the energy transition.

1. Domestic calorimetry: Heat $0.5\text{ kg}$ of water in a saucepan for $3\text{ min}$. Measure $T_i$ and $T_f$ (or take the boiling temperature) and calculate the useful heat absorbed using $Q = m \times c_e \times \Delta T$.

2. Hess, bonds and the first law: Calculate the molar enthalpy of combustion ($\Delta H^\circ$) of the gas used (butane or methane) by applying Hess's law or bond energies. Estimate the expansion work ($W = -\Delta n_g R T$) of the gases produced and deduce $\Delta U$. Determine the thermal efficiency of your stove by estimating the energy supplied from the burner's rated power (or the gas consumed) during the $3\text{ min}$.

3. Entropy and spontaneity: Look up the ambient temperature of your city on the National Weather Service website. Using tabulated standard thermodynamic data, calculate $\Delta S^\circ$ and $\Delta G^\circ$ at that temperature and explain the spontaneity of the process.

4. Technical proposal: Write a reasoned report (one page) with comparative tables, justifying the heat losses and suggesting practical energy-saving measures.

Assessment criteria:

• Rigor in setting up and calculating thermodynamic variables ($Q$, $W$, $\Delta H^\circ$, $\Delta S^\circ$ and $\Delta G^\circ$).

• Handling and consistency of the home experimental data and the official meteorological data (National Weather Service).

• Capacity for critical analysis when interpreting the thermal efficiency and the spontaneity of the system.