Question

Write the equation that states the first law of thermodynamics. In your own words, what does this statement mean in terms of energy exchanges between a system and its surroundings?

Short answer

The first law of thermodynamics is given by the equation \(\Delta U = Q - W\). It means that the energy within a closed system is conserved, with energy changes accounted for by heat exchange and work done.

Step-by-step solution

State the First Law of Thermodynamics

Write the equation for the first law of thermodynamics, which is expressed as \(\Delta U = Q - W\), where \(\Delta U\) represents the change in the internal energy of the system, \(Q\) is the heat added to the system, and \(W\) is the work done by the system on its surroundings.

Interpret the First Law

Explain the meaning of the first law of thermodynamics in terms of energy exchange. The law implies that the change in the internal energy of a system is equal to the heat added to the system minus the work done by the system. This means that the total energy of an isolated system is conserved and that energy can neither be created nor destroyed, only transferred or converted from one form to another.

Key concepts

Internal Energy

Internal energy is the total energy stored within a system due to the motion and arrangement of the molecules that make it up. This energy is the sum of the kinetic energy, owing to the movement of particles, and the potential energy, coming from the forces that act between them. When we look at the first law of thermodynamics, \(\Delta U = Q - W\), \(\Delta U\) signifies the change in this internal energy. If heat is added to the system, it can increase the internal energy by making the particles move more vigorously or changing their arrangements. Conversely, when the system does work on its surroundings, it can lose energy, resulting in a decrease in internal energy. Understanding that internal energy can vary with temperature, phase changes, and even chemical reactions is crucial for grasping the subtleties of energy flow within a physical system.

In practical terms, if you heat a gas in a sealed container, its internal energy will increase since the particles are moving faster and exerting greater pressure on the container walls. However, if the gas then expands and pushes on a piston (doing work), the internal energy decreases.

Energy Conservation

The principle of energy conservation is a fundamental concept in physics and a cornerstone of the first law of thermodynamics. Energy conservation states that energy can neither be created nor destroyed in an isolated system, it can only be transformed from one form to another or transferred from one object to another. This means the total amount of energy in a closed system remains constant over time.

When applied to the first law, \(\Delta U = Q - W\), energy conservation tells us that the heat energy \(Q\) added to a system and the work done \(W\) by that system are responsible for changes in the system's internal energy \(\Delta U\) but do not 'create' energy out of nothing. Instead, they convert it from thermal energy to mechanical energy or vice versa. This understanding ensures that when solving problems related to energy changes, the total energy will always remain balanced, which is a key to many scientific calculations, from engineering to environmental science.

Heat Exchange

Heat exchange refers to the transfer of thermal energy from one body or system to another due to the temperature difference. In terms of the first law of thermodynamics, \(Q\) stands for the quantity of heat exchanged. When heat is added to a system, it's considered positive, while heat lost by the system is negative.

Heat can be transferred through different processes such as conduction, convection, and radiation. For example, if a hot metal rod is placed in contact with a cooler block of ice, heat will conduct from the rod to the ice, raising the ice's temperature and causing it to melt. This is a direct heat exchange by conduction. It's essential to understand that this heat transfer does not violate the conservation of energy. Instead, it is the mechanism by which energy is distributed between systems or parts of a system.

Work Done

In physics, 'work done' represents a transfer of energy caused by a force moving an object over a distance. It is an essential part of the first law of thermodynamics equation, \(\Delta U = Q - W\), and is denoted by \(W\). If a system does work on its environment, \(W\) is a positive value, indicating that energy is being transferred out of the system. Conversely, if work is done on the system, the value of \(W\) is negative, implying the system gains energy.

To illustrate, compressing a spring requires work; you apply a force to move the spring a certain distance against its natural tension. The energy you use to compress the spring is then stored as potential energy in the spring system. If the spring is released, it can do an equivalent amount of work on another object, like pushing a ball, converting potential energy back into kinetic energy. Understanding the concept of work is vital for analyzing real-world systems, like engines and turbines, where work and energy transfer are continuous processes.