Some of the butane, C4 H10(g), in a 200.0 L cylinder at...

Some of the butane, $\mathrm{C}_{4} \mathrm{H}_{10}(\mathrm{g}),$ in a $200.0 \mathrm{L}$ cylinder at $26.0^{\circ} \mathrm{C}$ is withdrawn and burned at a constant pressure in an excess of air. As a result, the pressure of the gas in the cylinder falls from 2.35 atm to 1.10 atm. The liberated heat is used to raise the temperature of $132.5 \mathrm{L}$ of water in a heater from 26.0 to $62.2^{\circ} \mathrm{C}$ Assume that the combustion products are $\mathrm{CO}_{2}(\mathrm{g})$ and $\mathrm{H}_{2} \mathrm{O}(1)$ exclusively, and determine the efficiency of the water heater. (That is, what percent of the heat of combustion was absorbed by the water?)

Key Concepts

Energy Efficiency

Energy efficiency is the ratio of the useful output energy to the total energy input. In thermal systems, this concept measures how effectively heat produced from a chemical reaction is transferred and utilized for a specific purpose, such as heating water, compared to the energy originally released. It is a critical measure for evaluating the performance of energy conversion devices and processes.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas. This principle is essential for determining how variations in pressure and temperature, while keeping volume fixed or vice versa, affect the quantity of gas present. It allows for the calculation of the change in moles when a gas is either introduced or withdrawn from a fixed container, which is key in many thermodynamic processes.

Chemical Thermodynamics

Chemical thermodynamics is the study of energy changes, particularly the heat flow associated with chemical reactions. In combustion, this concept helps to quantify the heat released when fuel undergoes an exothermic reaction. Understanding the energy change during a reaction is crucial for calculating the total heat available from a reaction and for comparing it with the energy actually utilized.

Calorimetry

Calorimetry is the measurement of heat transfer during physical or chemical processes. It involves determining the amount of heat absorbed or released by a medium—in many cases, by measuring the temperature change in a substance like water. This technique applies the conservation of energy principle and is used to assess how much of the energy from a process is effectively captured in a thermal reservoir.

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