What is the primary difference between 'useful' energy and 'wasted' energy in a system?

Useful energy is the energy transferred to the specific store required for the system's intended purpose, while wasted energy is energy transferred to non-useful stores, typically dissipated as heat to the surroundings.

How does a Sankey diagram visually distinguish between a high-efficiency system and a low-efficiency system?

In a high-efficiency system, the horizontal 'useful' arrow is much wider than the 'wasted' arrows. In a low-efficiency system, the downward 'wasted' arrows are wider than the horizontal 'useful' arrow.

When calculating efficiency using a ratio, why is it sometimes unnecessary to convert kilojoules (kJ) to joules (J)?

Because efficiency is a ratio of two values with the same units, the units cancel out. As long as both the numerator and denominator use the same unit (both kJ or both J), the numerical result remains identical.

What is the most common mistake made when using the efficiency formula with percentages?

Students often forget to multiply the decimal ratio by 100 to get the percentage, or they accidentally place the total input in the numerator instead of the denominator.

What error occurs if you draw a Sankey diagram where the sum of the output arrow widths is greater than the input arrow width?

This violates the Law of Conservation of Energy, as it implies that energy was created within the system. The total width of all output arrows must exactly equal the width of the input arrow.

Why is it incorrect to say a machine is 110% efficient?

Efficiency over 100% implies that the machine is outputting more energy than it receives, which is physically impossible according to the first law of thermodynamics.

Define 'Efficiency' in the context of energy transfer.

Efficiency is the ratio of the useful energy or power output from a system to the total energy or power input supplied to it.

What does the width of an arrow represent in a Sankey diagram?

The width (or thickness) of the arrow represents the magnitude or amount of energy or power being transferred at that stage.

State the formula for efficiency in terms of power.

$$\text{Efficiency} = \frac{\text{Useful Power Output}}{\text{Total Power Input}} \times 100\%$$

How do you calculate wasted energy if you only know the total input and the useful output?

Wasted energy is calculated by subtracting the useful energy output from the total energy input ($E_{wasted} = E_{total} - E_{useful}$).

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Sankey Diagrams & Efficiency

Summary

Efficiency is a quantitative measure of how effectively a system transfers input energy into useful output energy. Sankey diagrams provide a visual framework for these transfers, where the width of arrows represents the magnitude of energy, allowing for a clear distinction between useful work and dissipated waste.

1. Definition & Core Concepts

Efficiency is defined as the ratio of useful energy (or power) output to the total energy (or power) input supplied to a system. It indicates what percentage of the original energy store is successfully converted into the intended form of work.
In every real-world energy transfer, some energy is dissipated or 'wasted,' usually as thermal energy transferred to the surroundings. This means no macroscopic system is 100% efficient due to the laws of thermodynamics.
Energy Stores: Systems operate by transferring energy from an input store (like chemical energy in fuel) to an output store (like kinetic energy in a motor or electrical energy in a generator).

A Sankey diagram showing a thick input arrow splitting into a horizontal 'Useful Output' arrow and a downward 'Wasted Energy' arrow. The width of the arrows represents the energy quantity.

2. Underlying Principles

3. Methods & Techniques

Calculating Efficiency

Step 1: Identify the total energy or power input. This is the 'cost' or the total amount of energy the system consumes.
Step 2: Identify the useful energy or power output. This is the specific form of energy the system was designed to produce (e.g., light from a bulb, kinetic energy from a car).
Step 3: Apply the efficiency formula:

$\text{Efficiency} = \frac{\text{Useful Energy Output}}{\text{Total Energy Input}} \times 100\%$

Step 4: Ensure units are consistent. If the input is in kilojoules (kJ), the output must also be in kJ for the ratio to be valid.

Interpreting Sankey Diagrams

Arrow Width: The vertical thickness of the arrow is directly proportional to the amount of energy. A wider arrow represents more Joules.
Directionality: Horizontal arrows typically represent the intended useful output, while arrows curving downwards or away from the main path represent energy dissipated to the surroundings.

4. Key Distinctions

5. Exam Strategy & Tips