Work

id: 1721571098
Date: April 23, 2025, 6:14 p.m.
Author: Donald F. Elger

Goals

Describe work
Skillfully use the concept of work for practical tasks: design, problem solving, math modeling and such

Work (What)

Work is any energy transfer at a system boundary that is not heat transfer.

In practical terms, work is a force acting over at distance or flow of electricity and so on. Thus, work is useful for many things: running a chain saw, powering a car, pumping water, moving a conveyer belt, and so on.

Analysis of the Definition

Here is a breakdown of the nomenclature in the definition.

Energy Transfer: An interaction at a system boundary that adds or removes energy from the matter inside the system.
Energy: Energy is a property of matter that characterizes the sum total of the heat plus work that can be done with this matter .
System: A system is matter of fixed identity that has been identified for analysis. Everything else in the universe is the surroundings.
Boundary: Interface between the system and its surroundings.
Heat Transfer: The transfer of thermal energy from hot to cold that is driven by a temperature difference.

Rationale

It is super useful to understand work because this knowledge can be applied to design machines etc. that do work for us. Also, this is key for understanding and applying energy.

Skill with Work (How To)

Think about work and do calculating by tying everything to the first law of thermo

Types of Work

Here are some common types of work.

Mechanical Work

Force acting over a distance. The formula for work is \(W=Fd\) in simple cases and in general \[ W = \int{\mathbf{F} \cdot \mathbf{dx}} \]

\(Pv\) Work (Work of a Piston)

This is the work associated with the expansion or compression of a gas within a piston-cylinder assembly. It is given by the integral of pressure over the change in volume:

\[W = \int_{V_i}^{V_f} P dV\]

where \(V_i\) and \(V_f\) are the initial and final volumes, respectively.

Shaft Work

Shaft Work: This occurs in devices like turbines, compressors, and pumps, where the work is done by the rotating shaft.

Electrical Work

This is the work done when a electric current passes across a system boundary.

Sign Convention

In thermodynamics, the sign convention for work is crucial:

Positive Work: Work done by the system on the surroundings (e.g., expansion of a gas).
Negative Work: Work done on the system by the surroundings (e.g., compression of a gas).