Question

A certain system absorbs \(0.300 \mathrm{~kJ}\) of heat and has \(0.700 \mathrm{~kJ}\) of work performed on it. What is the value of \(\Delta E\) for the change? Is the overall change exothermic or endothermic?

Short answer

\(\Delta E = 1.000 \mathrm{~kJ}\), and the overall change is endothermic.

Step-by-step solution

Understand the First Law of Thermodynamics

The First Law of Thermodynamics, also known as the law of energy conservation, states that the total energy change \(\Delta E\) in a system is the sum of the heat \(q\) added to the system and the work \(w\) done on the system. The mathematical representation is \(\Delta E = q + w\).

Identify the Known Quantities

From the problem, identify the amount of heat absorbed by the system \(q = 0.300 \mathrm{~kJ}\) and the amount of work performed on it \(w = 0.700 \mathrm{~kJ}\).

Calculate the Change in Internal Energy

Using the formula \(\Delta E = q + w\), substitute the known values to calculate the energy change: \[\Delta E = 0.300 \mathrm{~kJ} + 0.700 \mathrm{~kJ} = 1.000 \mathrm{~kJ}\]

Determine the Nature of the Change

Since the system absorbs heat, the process is endothermic. An endothermic process is characterized by a positive heat flow into the system.

Key concepts

Energy Conservation

In the realms of physics and chemistry, the principle of energy conservation is a foundational concept. It is succinctly encapsulated by the First Law of Thermodynamics, which asserts that energy cannot be created nor destroyed in an isolated system. Rather, energy can only be transformed or transferred from one form to another. This tenet is vital both for conceptual understanding and practical calculations in science.

To apply this to our context, when a system, such as a gas or a chemical reaction, absorbs heat or has work performed on it, the system's total energy shifts by an amount that exactly matches the sum of heat and work involved. Therefore, the change in the system's internal energy, denoted \(\Delta E\), is always the result of this balance. Translating this into a mathematical formula gives us \(\Delta E = q + w\), where \(q\) represents heat and \(w\) signifies work.

Internal Energy Change

The concept of internal energy change is central to understanding how energy is stored and transformed within a system. Internal energy, symbolized as \(E\), is the sum of the potential and kinetic energies of all particles within a system. When we talk about the change in internal energy, \(\Delta E\), we are referring to the difference between the internal energy at the final state and at the initial state of a process.

In the example provided, \(\Delta E\) signifies the net change due to external influences: heat absorption and the performance of work. This thermodynamic parameter, \(\Delta E\), allows us to gauge the energy alterations within the system without needing to inspect each microscopic interaction. It's the macroscopic view of how energy shifts from the surroundings to the system (or vice versa) and reveals whether the system's energy has increased or decreased after a certain process.

Endothermic Process

An endothermic process is characterized by the absorption of heat. During such a process, a system gains energy from its surroundings, typically in the form of heat (\(q\)), resulting in an increase in the system's internal energy. This is why we often associate endothermic processes with a sense of coldness in the surroundings—the system is literally absorbing heat from around it.

In the context of our exercise, we identified that heat is being absorbed (\(q = 0.300 \mathrm{~kJ}\)). Concurrently, work is also done on the system (\(w = 0.700 \mathrm{~kJ}\)), thus further contributing to the increase in internal energy. The total energy gained by the system is \(1.000 \mathrm{~kJ}\), which definitely classifies the transformation as endothermic. Endothermic reactions or processes are critical to chemical thermodynamics, as they help to describe interactions where energy input is necessary for a reaction to occur.