A geyser, operating on LPG (liquefied petroleum gas) heats water flowing at the rate of \(3.0\) litres per minutes, from \(27^{\circ} \mathrm{C}\) to \(77^{\circ} \mathrm{C}\). If the heat of combustion of LPG is \(40,000 \mathrm{~J} / \mathrm{g}\), how much fuel, in \(\mathrm{g}\), is consumed per minute? (Specific heat capacity of water is \(4200 \mathrm{~J} / \mathrm{kg}-\mathrm{K}\) ) (a) \(15.25\) (b) \(15.50\) (c) \(15.75\) (d) \(16.00\)

In the realm of thermochemistry, specific heat capacity is a pivotal concept that defines how much energy is needed to raise the temperature of 1 kilogram of a substance by 1 degree Celsius (or 1 Kelvin). From a practical standpoint, it tells us why different materials heat up at different rates. For instance, metal feels hotter than wood when both are exposed to sunlight because metal has a lower specific heat capacity, allowing it to heat up more quickly.

Understanding specific heat capacity is crucial when we tackle problems involving temperature change. In our exercise, we're given the specific heat capacity of water, which is unusually high at 4200 J/kg-K. This property is what makes water an excellent medium for thermal storage, such as in our geyser example. It absorbs a lot of energy for a relatively small temperature rise, ensuring the water heats evenly.

Another key term in our exploration of thermochemistry is the heat of combustion. This represents the amount of energy released when a certain mass of a substance is burned. It's a measure of the fuel's 'energy density.' In our geyser problem, we look at LPG, which has a given heat of combustion of 40,000 J/g.

By applying this information, we can determine how much LPG is needed to generate a certain amount of heat. This data allows individuals and industries to calculate fuel requirements for various heating processes. For example, understanding the heat of combustion for LPG enables us to assess the cost-effectiveness and efficiency of LPG geysers, as seen in this exercise.

The concept of energy transfer in chemistry is at the heart of any thermochemical process. It encompasses the way energy moves from one substance to another, such as during the heating or cooling of materials. Specifically, our exercise involves energy transfer from the combustion of LPG to water, resulting in an increase in water temperature.

Energy transfer is not just about the quantity of energy but also about its efficient utilization. That's why we calculate how much fuel is consumed per minute; it's a direct measure of the efficiency of energy transfer in our geyser system. A good understanding of energy transfer can also help in devising ways to minimize energy losses and improve overall energy efficiency in various applications.

Finally, physical chemistry exercises, such as the one we're discussing, are designed to apply theoretical knowledge to real-world scenarios. These exercises reinforce understanding by pushing students to use equations and concepts to solve practical problems. The exercise in question not only engages with specific heat capacity and the heat of combustion but also pulls in the conservation of energy principle and mathematical problem-solving.

For anyone seeking to master physical chemistry, these exercises are invaluable. They demonstrate how concepts interlink and influence actual systems, preparing students for the kind of thinking required in professional scientific work. As we break down the problems into step-by-step solutions, we aim to make complex phenomena understandable and show how the physical world obeys clear, quantifiable rules.