Question

State the first law of thermodynamics in your own words. What equation defines the change in the internal energy in terms of heat and work? Define the meaning of the symbols, including the significance of their algebraic signs.

Short answer

The first law of thermodynamics states that the change in internal energy of a closed system (\(\Delta U\text{)} is equal to the heat added to the system (\text{Q}) minus the work done by the system (\text{W}), expressed as \(\Delta U = Q - W\). Positive \text{Q} indicates heat entering the system, while positive \text{W} indicates work done by the system.

Step-by-step solution

State the First Law of Thermodynamics

The first law of thermodynamics can be articulated as: In a closed system, the total increase in the internal energy is equal to the sum of the energy added to the system as heat and the energy lost by the system as work. This law is a statement of the conservation of energy, indicating that energy can neither be created nor destroyed, only transferred or transformed.

Define the Equation

The equation that defines the change in the internal energy \(\Delta U\) in terms of heat \(Q\) and work \(W\) is expressed as: \[\Delta U = Q - W\] This equation quantifies the first law of thermodynamics, illustrating how internal energy changes within a system.

Define the Symbols and Their Significance

In the equation \(\Delta U = Q - W\): \(\Delta U\) symbolizes the change in internal energy of the system; \(Q\) represents the heat added to the system, where a positive value signifies heat entering the system, and a negative value represents heat exiting the system; \(W\) signifies the work done by the system, where a positive value indicates work done by the system on the surroundings, and a negative value denotes work done on the system by the surroundings. The algebraic signs reflect the direction of energy transfer.

Key concepts

Internal Energy

When discussing the first law of thermodynamics, it's crucial to comprehend the concept of internal energy. Internal energy, often denoted as U, pertains to the total energy contained within a system due to both the kinetic and potential energies of its molecules. This energy is a cumulative variable, encompassing everything from molecular vibrations and rotations to intermolecular forces.

Changes in internal energy can occur without apparent external effects, such as temperature or volume alterations; these changes are a result of energy interactions like heat exchange or work performed. In essence, when a system undergoes a transformation, such as heating, cooling, or physical labor exerted on or by the system, its internal energy will alter accordingly. While we cannot measure the absolute value of internal energy directly, we can certainly assess the change in internal energy, represented as \( \Delta U \).

This evaluation is critical because it ties back to our exercise: the ascertainable change in a system's energy is ascribed to heat added or work done, which leads to the fundamental understanding of the first law.

Heat and Work in Thermodynamics

Delving deeper into the first law of thermodynamics, let's focus on the role of heat and work as they relate to the law. In the realm of thermodynamics, heat (Q) signifies the transfer of energy due to a temperature difference between a system and its surroundings. It's one of the ways energy can enter or leave a system.

The second primary way is through work (W), which in thermodynamics is the energy transfer that occurs when a force moves an object over a distance. It's essential to understand that work here can be piston movement, electrical work, or any other type encompassing a force causing a displacement.

Understanding Sign Conventions

In thermodynamics, the sign of Q and W is significant. A positive Q indicates heat is added to the system, while a negative Q denotes heat leaving. Similarly, a positive W implies work done by the system, and a negative W signifies work done on the system. This convention ensures that the first law's equation, \(\Delta U = Q - W\), accurately reflects the direction of energy transfer into or out of the system, with \(\Delta U\) accounting for both heat and work.

Conservation of Energy

The backbone of the first law of thermodynamics is the conservation of energy principle. This fundamental doctrine asserts that energy in a closed system remains constant; it can neither be created out of thin air nor vanish into nothingness. Instead, energy is only converted from one form to another or transferred from one part of the system to another or to its surroundings.

Understanding the conservation of energy is pivotal—it's the scientific rationale for the first law's equation. When the internal energy of a system changes, it's due to the transformation or movement of energy, not its magical appearance or disappearance. For instance, when you rub your hands together, the mechanical energy from the movement is not lost but transformed into heat energy, which is experienced as warmth.

This concept doesn’t only apply to simple systems but also underpins complex processes across physics, chemistry, and biology, highlighting the unbreakable rule that energy continues on its journey from one form to another, perpetually conserved.