1.2 Thermodynamic systems and surroundings

Thermodynamic Systems and Surroundings

A thermodynamic system is simply the region or quantity of matter you choose to analyze. Everything else is the surroundings. The boundary between them determines what can cross (energy, mass, or neither), and that distinction shapes every calculation you'll do in this course.

Types of Thermodynamic Systems

A thermodynamic system is a region in space or a quantity of matter enclosed by a boundary (real or imaginary). There are three types, classified by what they allow across that boundary:

• Open system: Both energy and mass can cross the boundary. Think of a turbine in a power plant: steam flows in, does work on the blades, and exits. A pot of boiling water is another example, since steam (mass) escapes and heat (energy) enters from the stove.
• Closed system: Energy can cross the boundary, but mass cannot. A sealed piston-cylinder device is the classic example. The gas inside can be heated or compressed (energy transfer), but no gas enters or leaves. A pressure cooker before its valve opens works the same way.
• Isolated system: Neither energy nor mass can cross the boundary. A perfectly insulated, sealed container fits this description. In reality, truly isolated systems don't exist, but a high-quality thermos flask comes close. This idealization is useful because the total energy inside an isolated system stays constant.

Boundaries in Thermodynamic Systems

The system boundary is the surface (real or imaginary) that separates the system from its surroundings. You get to choose where this boundary goes, and your choice depends on what you're trying to analyze.

The surroundings are everything outside that boundary. The surroundings can exchange energy and/or mass with the system, depending on the system type.

When you set up a thermodynamic problem, follow these steps:

1. Define the system of interest. What region or quantity of matter are you analyzing? (e.g., the gas inside a cylinder, the water flowing through a pipe)
2. Draw the system boundary. Make it clear what's inside and what's outside. This can be a physical wall (like a piston) or an imaginary surface you define.
3. Identify the interactions across the boundary. Is heat ($Q$) crossing? Is work ($W$) being done? Is mass flowing in or out?

Getting this setup right is half the battle. A poorly chosen boundary makes the problem harder than it needs to be.

System-Surroundings Interactions

Energy crosses a system boundary in two forms:

• Heat ($Q$): Energy transfer driven by a temperature difference between the system and surroundings. Heat flows from hot to cold.
• Work ($W$): Energy transfer caused by a force acting through a distance. A piston compressing gas, a shaft turning, or an electrical current entering the system are all forms of work.

Mass transfer occurs only in open systems. Matter physically enters or leaves the system, carrying energy with it (more on this in the control volume section below).

When analyzing any interaction, you need to:

1. Determine the direction of each transfer. Is energy entering or leaving the system? Is mass flowing in or out?
2. Assess the effect on system properties. Does the temperature rise? Does the pressure change? Does the volume expand?
3. Apply conservation principles. Energy and mass are conserved, so everything entering, leaving, and stored must balance.

Control Volume in Thermodynamics

A control volume is a fixed region in space through which matter may flow. It's the standard tool for analyzing open systems. Instead of tracking a specific chunk of fluid as it moves, you watch what flows into and out of a defined region.

The two key conservation equations for a control volume are:

Conservation of mass:

$\frac{dm_{cv}}{dt} = \sum \dot{m}_{in} - \sum \dot{m}_{out}$

This says the rate of mass change inside the control volume equals mass flowing in minus mass flowing out.

Conservation of energy:

$\frac{dE_{cv}}{dt} = \dot{Q}_{cv} - \dot{W}_{cv} + \sum \dot{m}_{in}\left(h + \frac{V^2}{2} + gz\right)_{in} - \sum \dot{m}_{out}\left(h + \frac{V^2}{2} + gz\right)_{out}$

Here, $h$ is specific enthalpy, $\frac{V^2}{2}$ is specific kinetic energy, and $gz$ is specific potential energy. Each mass stream carries these forms of energy with it.

Steady-state is a common simplification. If conditions inside the control volume aren't changing with time, both time derivatives become zero. This means mass in equals mass out, and the energy equation simplifies significantly. Most textbook problems involving turbines, compressors, and heat exchangers assume steady state.

To solve a control volume problem:

1. Define the control volume and sketch its boundaries.
2. Identify all inlets and outlets where mass crosses the boundary, plus any heat or work interactions.
3. Determine whether the process is steady-state or transient. Steady-state sets the time derivatives to zero; transient problems require you to keep them.
4. Apply the conservation equations and solve for the unknowns.