First Law of Thermodynamics (Amount Form)

First Law (What?)

The first law of thermodynamics asserts that the change in energy for a system is balanced by the heat into the system from its surroundings minus the work done by the system on its environment.

ΔE = Q − W {#eq-first-law-amount-form}

• System: A system is whatever matter you select to analyze.
• ΔE: Change in energy of the matter within the system (J).
• Q: Amount of heat transferred from the surroundings to the system (J).
• W: Amount of work done by the system on its surroundings.

Rationale

Here are some reasons why this equation is worth learning.

1. Application: This equation is one of the most commonly used equations in engineering and might be among the top five, perhaps even number one. It is super-useful.

2. General Form: The first law of thermodynamics can be written in many forms. However, all of these forms can be derived from @eq-first-law-amount-form. Thus, I recommend learning this form and then over time learning how to derive the myriad of other forms.

How to Apply the First Law

Applying @eq-first-law-amount-form involves analyzing the three terms and plugging numbers in if calculations are involved. However, there are a huge number of details that are needed for doing this skillfully. I will present these details throughout this BookCourse because presenting them now would likely be overwhelming for most learners.

Facts

Justification

The first law of thermodynamics, also known as the law of energy conservation, is accepted as true because countless experiments have proven it to be true. This acceptance is based on empirical evidence. The law was first articulated around 1850 by Rudolf Clausius and is credited to multiple researchers, including James Joule and Hermann von Helmholtz. Joule’s experiments on the mechanical equivalent of heat and Helmholtz’s work on the conservation of energy provided substantial evidence for this principle. Clausius’s formulation mathematically expressed the relationship between heat, work, and internal energy, solidifying its foundational role in thermodynamics.

When to Apply This

There are no assumptions required. Therefore, apply it whenever it is useful.

Amount Form (System)

I call this equation the “amount form” of the first law for a “system” or “closed system.” Here are the reasons why.

• Amount Form: In this form, the equation is used to track amounts of energy, work, and heat. The units are joules. In other forms, the units are watts, and the equation is used to balance rates. This form is called the rate form.
• (Closed) System: All systems in engineering are either open or closed. Multiple forms of the first law apply to an open system, also known as a control volume. Most engineers, when they speak of a system, are referring to a closed system. When they refer to an open system, they use either “control volume” or “open system” to identify what they mean.

Summary

The first law of thermodynamics is one of the most useful relationships in all of engineering. This law states that the energy change for a system (ΔE) is balanced by the heat added to the system (Q) minus the work done by the system on its surroundings (W). This equation is applied by analyzing each of its terms. This equation always applies.