Question

What are possible boundaries for studying each of the following? (a) a bicycle tire inflating. (b) a cup of water being heated in a microwave oven. (c) a household refrigerator in operation. (d) a jet engine in flight. (e) cooling a desktop computer. (f) a residential gas furnace in operation. (g) a rocket launching.

Short answer

Boundaries can include entire systems: tire and pump, water and cup, refrigerator, jet engine, computer case, gas furnace, and entire rocket.

Step-by-step solution

- Define boundaries for bicycle tire inflating

Consider the tire and air pump system. The possible boundary could be around the entire tire and pump setup which includes the internal air space, the pump mechanism, and the tire material.

- Define boundaries for a cup of water being heated in a microwave oven

Identify the boundaries as the cup and the water it contains. The boundary could also include the microwave oven chamber, but focusing on the cup and its water for study seems sufficient.

- Define boundaries for a household refrigerator in operation

The refrigerator boundaries should include the entire appliance, encompassing the internal cooling compartments, the insulation, and the external surface.

- Define boundaries for a jet engine in flight

The boundaries can be set around the entire jet engine. This includes the inlet, compressor, combustion chamber, turbine, and exhaust sections.

- Define boundaries for cooling a desktop computer

Establish boundaries around the entire computer case. This includes internal components such as the CPU, GPU, cooling fans, and heat sinks.

- Define boundaries for a residential gas furnace in operation

Consider the gas furnace as the primary boundary. Include the heat exchanger, burner, and venting system as part of the furnace's boundaries.

- Define boundaries for a rocket launching

The boundaries should encompass the entire rocket, including the propulsion system, fuel tanks, payload, and control systems.

Key concepts

thermodynamic systems

In thermodynamics, a system refers to the part of the universe that is being studied. Everything outside this system is known as the surroundings. Systems are categorized based on how they interact with their surroundings. There are three main types:

• Open Systems: These can exchange both energy and matter with their surroundings. For instance, a boiling pot of water with the lid off.
• Closed Systems: These can exchange energy, but not matter, with the surroundings. A tightly sealed, yet heated, bottle of soda is an example.
• Isolated Systems: These do not interact with their surroundings in any way. Practically, perfect isolated systems are hard to achieve, but a well-insulated thermos flask approximates it.

Choosing the right system type depends on the scenario we wish to study, like defining boundaries for a bicycle tire inflating or a jet engine in flight.

control volume

A control volume is a specified region in space where we analyze the flow of matter and energy. It’s particularly useful in fluid mechanics and thermodynamics. For example:

• Bicycle Tire Inflating: The control volume could encapsulate the tire and the pump. This lets us study how air flows into the tire and how the pressure changes.
• Jet Engine in Flight: Here, a control volume would likely include the entire engine, capturing how air enters, mixes with fuel, combusts, and exits as exhaust.

Defining the boundaries of the control volume is crucial, as it helps in simplifying the analysis and making accurate predictions about the system’s behavior over time.

heat transfer

Heat transfer is the process by which thermal energy moves from one place to another. There are three primary modes:

• Conduction: Heat flows through a solid material, like a spoon in hot soup.
• Convection: Heat transfer occurs due to the movement of fluid, such as heating water in a microwave.
• Radiation: Thermal energy travels via electromagnetic waves, like the warmth felt from the sun.

When studying systems like a cup of water being heated in a microwave or a refrigerator in operation, understanding these modes helps us delineate energy flow and efficiency. Selecting appropriate boundaries assists in isolating and analyzing the mode that plays a dominant role in each scenario.

fluid mechanics

Fluid mechanics is the study of fluids (liquids and gases) at rest and in motion. Key concepts include:

• Viscosity: A fluid’s resistance to flow. Water has low viscosity, whereas honey has high viscosity.
• Flow Rate: The volume of fluid passing a point per unit time, crucial for understanding cooling systems in computers or gas furnaces.
• Bernoulli’s Principle: As fluid speed increases, pressure decreases. This principle aids in understanding the aerodynamics of a jet engine.

For example, fluid mechanics underpins how air enters and exits a rocket during launch, affecting its propulsion and stability. Clearly defined boundaries help in accurately capturing these parameters.

energy analysis

Energy analysis involves quantifying how energy enters, transforms, and leaves a system. The first law of thermodynamics, or the conservation of energy, is key here. It states that energy cannot be created or destroyed—only transformed from one form to another. Key steps include:

• Identify Energy Sources: Determine where the energy is coming from, like electrical energy in a desktop computer or chemical energy in a gas furnace.
• Analyze Energy Conversion: Understand how energy is converted within the system. For instance, kinetic energy in a rocket’s fuel converts to mechanical energy thrust.
• Calculate Energy Losses: Identify any energy losses due to inefficiencies, such as heat loss in a gas furnace or resistive losses in electrical systems.

Applying these steps, you can analyze and optimize systems such as a refrigerator in operation or heating a cup of water in a microwave.