Question

When 1 mol of a fuel burns at constant pressure, it produces \(3452 \mathrm{~kJ}\) of heat and does \(11 \mathrm{~kJ}\) of work. What are \(\Delta E\) and \(\Delta H\) for the combustion of the fuel?

Short answer

Delta E = 3452 kJ - 11 kJ = 3441 kJ, Delta H = 3452 kJ

Step-by-step solution

Calculate the Change in Internal Energy (Delta E)

According to the first law of thermodynamics, the change in internal energy (Delta E) of a system is equal to the heat (q) added to the system minus the work (w) done by the system on its surroundings. This can be written as: Delta E = q - w. Given that the heat produced is 3452 kJ and the work done is 11 kJ, we can substitute these values into the equation to get Delta E.

Calculate the Change in Enthalpy (Delta H)

At constant pressure, the change in enthalpy (Delta H) is equal to the heat (q_p) that is exchanged. Therefore, Delta H is equal to the heat produced during the combustion process, which is given as 3452 kJ.

Key concepts

Change in Internal Energy

In thermodynamics, the internal energy of a system is the total of all forms of energy present within it. It's an extensive property, meaning it depends on the amount of matter in the system. The change in internal energy, denoted as \(\text{\Delta} E\), encapsulates how the internal energy shifts due to interactions like heat transfer or work done by or on the system.

Consider our exercise where a fuel's combustion releases \(3452 \mathrm{~kJ}\) of heat and does \(11 \mathrm{~kJ}\) of work. To calculate the change in internal energy, we subtract the work done from the heat produced: \(\text{\Delta} E = q - w\). Thus, \(\text{\Delta} E = 3452 \mathrm{~kJ} - 11 \mathrm{~kJ} = 3441 \mathrm{~kJ}\). This indicates the net amount of energy that gets stored in the system after the combustion.

First Law of Thermodynamics

The first law of thermodynamics, also known as the law of energy conservation, establishes the principle that energy can neither be created nor destroyed, only transformed. It provides a relationship between the heat absorbed or released by a system and the work it performs on its surroundings, or that is done on it.

Following this principle, our exercise states that the fuel combustion at constant pressure results not just in the release of heat, but also in the system performing work. Intuitively, we can see the first law in action: the energy that was contained in the fuel's chemical bonds is converted into thermal energy, and some of it becomes mechanical energy that does work. Therefore, the change in internal energy \(\text{\Delta} E\) will equal the heat \(q\) minus the work \(w\): \(\text{\Delta} E = q - w\). This law underpins the calculations in our exercise and is fundamental to understanding energy flow in chemical processes.

Change in Enthalpy

Enthalpy, denoted as \(H\), is a thermodynamic quantity equivalent to the total heat content of a system. It is linked to the internal energy of the system but also takes into account the pressure and volume of the system. The term \(\text{\Delta} H\) represents the change in enthalpy during a process.

In reactions occurring at constant pressure, like our exercise's combustion process, the change in enthalpy \(\text{\Delta} H\) reflects the heat exchanged with the surroundings. Here, the heat produced is entirely attributed to the change in enthalpy since no volume change occurs when the pressure is held constant. Consequently, \(\text{\Delta} H\) in our scenario is directly equal to the heat produced, \(3452 \mathrm{~kJ}\). Understanding \(\text{\Delta} H\) is crucial for processes involving heat transfer under constant pressure conditions.

Combustion Process

The combustion process is a high-temperature exothermic reaction where a fuel reacts with an oxidant, typically oxygen, releasing energy in the form of heat and light. Commonly, combustion refers to the burning of a fuel like gas, wood, or oil.

In our exercise, the combustion of 1 mole of fuel at constant pressure indicates a controlled environment typically found in calorimetry studies. The substantial release of energy (heat) measured as \(3452 \mathrm{~kJ}\), is indicative of the energy available in the chemical bonds of the fuel. This energy release is used not only to increase the internal energy of the products but also to do work on the surroundings, as denoted by the \(11 \mathrm{~kJ}\) of work performed. The details of the combustion process allow for insights into the energy changes during the reaction and are fundamental in fields such as energy engineering, environmental science, and thermochemistry.