Question

Which statement is true of the internal energy of the system and its surroundings following a process in which \(\Delta E_{\mathrm{sys}}\) \(=+65 \mathrm{kJ} ?\) Explain. \begin{equation} \begin{array}{l}{\text { a. The system and the surroundings both lose } 65 \text { kJ of energy. }} \\ {\text { b. The system and the surroundings both gain } 65 \text { kJ of energy. }} \\ {\text { c. The system loses } 65 \text { kJ of energy, and the surroundings gain } 65 \text { kJ of }} \\ {\text { d. The system gains } 65 \text { kJ of energy, and the surroundings lose } 65 \text { kJ of }} \\ {\text { energy. }}\end{array}\end{equation}

Short answer

The system gains 65 kJ of energy, and the surroundings lose 65 kJ of energy.

Step-by-step solution

Understanding Internal Energy Change

First understand that internal energy is a property of the system. A positive change in the internal energy (\(\triangle E_{\text{sys}} > 0\)) indicates that the system has gained energy.

Applying the Law of Conservation of Energy

According to the law of conservation of energy, energy cannot be created or destroyed, only transferred. If the system gained energy, then that energy must have come from its surroundings.

Identifying the Correct Statement

Comparing the given statements with our understanding, we can determine that the correct statement is the one where the system gains energy (which is a positive change in internal energy) and the surroundings lose an equal amount of energy.

Key concepts

Law of Conservation of Energy

The law of conservation of energy, a foundational principle in physics, states that energy cannot be created or destroyed in an isolated system; it can only be transformed from one form to another. This timeless concept holds true across all branches of physics and applies to all scenarios, including mechanical, electrical, thermal, and nuclear processes.

When analyzing any physical situation, one can employ this law to track where energy is moving. For instance, when a ball is thrown into the air, its kinetic energy is gradually converted into gravitational potential energy as it rises. When it stops at the peak and begins to fall, that potential energy is converted back into kinetic energy. Energy is not lost in the process; it just changes form. Similarly, in a closed system, when a process occurs such as a chemical reaction or a phase change, the total energy before the process is equal to the total energy after the process, when you sum up all forms including heat, work, internal, and potential energies.

Thermodynamics

Thermodynamics is the branch of physics that deals with the relationships and conversions between heat and other forms of energy. It encompasses a set of laws that describe how energy is transferred within and between systems.

One of the core concepts in thermodynamics is the idea of internal energy, symbolized as 'U' or 'E'. This internal energy is the total energy contained within a system, which includes kinetic energy due to the motion of molecules and potential energy due to the forces within or between molecules.

The first law of thermodynamics, also known as the principle of conservation of energy, asserts that the change in internal energy of a closed system is equal to the heat supplied to the system minus the work done by the system on its surroundings. In equation form, it is expressed as \( \triangle E_{\text{sys}} = Q - W \), where \( Q \) is the heat added to the system and \( W \) is the work done by the system.

Energy Transfer in Systems

Energy transfer in systems occurs in various ways, including heat transfer, work done by or on the system, and the flow of mass into or out of the system. In many educational problems, these transfers are simplified to just work and heat, as these are the primary means by which a system's internal energy changes in many processes.

When discussing heat transfer, it's essential to remember that heat flows spontaneously from a hotter object to a cooler one until thermal equilibrium is reached. The three modes of heat transfer are conduction, convection, and radiation. Work, on the other hand, may involve forces acting over distances, or in thermodynamic processes, it often pertains to the expansion or compression of gases.

Linking this back to the law of conservation of energy, if a system gains internal energy, then that energy must have been transferred from its surroundings; conversely, if a system loses internal energy, then that energy must have been transferred to its surroundings. Energy transfer is the key to understanding how systems interact with their environment, maintaining the balance prescribed by the law of conservation of energy.