Question

Which statement is true of the internal energy of a system and its surroundings during an energy exchange with a negative \(\Delta E _ { \text { sys } }\) ? a. The internal energy of the system increases, and the internal energy of the surroundings decreases. b. The internal energy of both the system and the surroundings increases. c. The internal energy of both the system and the surroundings decreases. d. The internal energy of the system decreases, and the internal energy of the surroundings increases.

Short answer

d. The internal energy of the system decreases, and the internal energy of the surroundings increases.

Step-by-step solution

Understand the Concept of Internal Energy Change

Internal energy changes in a system, denoted as \(\Delta E _ { \text{sys} }\), represent the total energy change of the system. A negative \(\Delta E _ { \text{sys} }\) means that the system has lost energy to its surroundings.

Analyze the Possible Outcomes

When a system undergoes an energy exchange and loses energy (negative \(\Delta E _ { \text{sys} }\)), the energy must be gained by the surroundings. Conversely, if the system gains energy, then the surroundings must lose energy.

Identify the Correct Statement Based on Energy Conservation

Using the law of conservation of energy, the loss of energy by the system must be equal to the gain in energy by the surroundings. Thus, if \(\Delta E _ { \text{sys} }\) is negative, then the system's internal energy decreases, and the surroundings' internal energy increases.

Key concepts

Thermodynamics

Thermodynamics is a branch of physics that deals with the relationships between heat and other forms of energy. In particular, it describes how thermal energy is converted to and from other forms of energy and how it affects matter. The primary laws of thermodynamics set the stage for understanding how energy systems operate and how they interact with their environment.

The first law of thermodynamics, also known as the law of energy conservation, states that energy cannot be created or destroyed, only transformed from one form to another. This principle is fundamental when examining the internal energy changes within a system. It helps explain the way energy is transferred between a system and its surroundings during an energy exchange. A negative change in a system's internal energy, indicated by a negative \( \Delta E _ { \text{sys} } \), reflects that the transfer is directed outward, meaning the system is relinquishing energy to its environment.

When studying thermodynamics in the context of internal energy changes, it's also essential to consider how the properties of a system—such as temperature and pressure—can affect the capacity for energy exchange. It also means that energy changes inevitably lead to changes in state or phase, affecting the system's overall internal energy as it absorbs or releases heat.

Energy Conservation

The concept of energy conservation is integral to understanding how various physical systems operate. Within the realm of thermodynamics, energy conservation is expressed through the first law, as previously mentioned. It asserts that the total amount of energy in a closed system remains constant—though energy may change forms, the total energy will be conserved.

When applying this concept to a system exchanging energy, as in the original exercise, it's crucial to recognize that a loss of energy in the system (\( \Delta E _ { \text{sys} } \)) results in an equivalent gain of energy in the surroundings. This trade-off aligns with energy conservation: the amount of energy lost by the system is equal to the amount gained by its surroundings, maintaining the overall energy balance.

It's important for students to learn that energy conservation doesn't solely apply to simple mechanical systems but extends to complex biological, chemical, or thermodynamic systems as well. Understanding these principles can help students unravel the workings of energy transfer in various scientific disciplines and real-world applications.

Delta E System

In thermodynamics, \( \Delta E _ { \text{sys} } \) represents a change in internal energy within a system. The \( \Delta \) symbol indicates a change or difference, while \( E \) denotes energy, and \( \text{sys} \) specifies the system in question. \( \Delta E _ { \text{sys} } \) can be positive, when the system gains energy, or negative, when the system loses energy. It's a vital concept that quantifies the extent of energy change during any process—whether through heat transfer, work done by or on the system, or a combination of both.

If a system exhibits a negative \( \Delta E _ { \text{sys} } \) during a process, it highlights that energy is flowing out of the system and into the surroundings. This corresponds to answer 'd' in the given exercise, stating that the system's internal energy decreases as it releases energy, whereas the internal energy of the surroundings increases as it absorbs that energy. The students can comprehend this concept by equating it to financial transactions within their accounts. Just as withdrawing money results in a decrease in account balance, a negative \( \Delta E _ { \text{sys} } \) implies a depletion of the system's energy reserves.