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Physics: Energy, Climate, and Sustainability - Sankey Diagrams and Energy Efficiency

Grade 8IB

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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The Law of Conservation of Energy states that energy cannot be created or destroyed, only transformed from one form to another. Therefore, the total energy input into a system must equal the total energy output: Etotal in=Euseful out+Ewasted outE_{\text{total in}} = E_{\text{useful out}} + E_{\text{wasted out}}.

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A Sankey Diagram is a visual representation of energy flow where the width of the arrows is directly proportional to the amount of energy. The thickest part represents the total energy input, while branches represent useful and wasted energy transfers.

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Energy Efficiency is a measure of how much of the input energy is converted into useful output energy. It is often expressed as a percentage: Efficiency%=(Useful EnergyTotal Energy)×100\text{Efficiency} \% = \left( \frac{\text{Useful Energy}}{\text{Total Energy}} \right) \times 100.

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Sustainability in physics involves improving energy efficiency to reduce the consumption of finite resources and minimize environmental impacts like climate change. Reducing 'wasted' energy (often dissipated as thermal energy) is a primary goal of sustainable design.

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Dissipation refers to the process where energy spreads out into the surroundings in less useful forms, such as heat and sound, making it harder to harness for work.

📐Formulae

Efficiency=Useful Energy OutputTotal Energy Input\text{Efficiency} = \frac{\text{Useful Energy Output}}{\text{Total Energy Input}}

Efficiency (%)=Useful Energy OutputTotal Energy Input×100\text{Efficiency (\%)} = \frac{\text{Useful Energy Output}}{\text{Total Energy Input}} \times 100

Etotal=Euseful+EwastedE_{\text{total}} = E_{\text{useful}} + E_{\text{wasted}}

Useful Energy Output=Total Energy Input×Efficiency (decimal)\text{Useful Energy Output} = \text{Total Energy Input} \times \text{Efficiency (decimal)}

💡Examples

Problem 1:

An electric motor takes in 25002500 J of electrical energy. It produces 18001800 J of useful kinetic energy and the rest is dissipated as heat and sound. Calculate the efficiency of the motor and the amount of wasted energy.

Solution:

Wasted Energy=2500−1800=700 J\text{Wasted Energy} = 2500 - 1800 = 700 \text{ J} Efficiency=18002500×100=72%\text{Efficiency} = \frac{1800}{2500} \times 100 = 72 \%

Explanation:

First, we use the conservation of energy to find the wasted energy by subtracting the useful output from the total input. Then, we divide the useful energy by the total input and multiply by 100100 to find the percentage efficiency.

Problem 2:

A Sankey diagram for a filament lamp shows 100100 J of electrical energy input. The arrow for light (useful energy) is 11 cm wide, and the arrow for heat (wasted energy) is 99 cm wide. Calculate the efficiency of the lamp.

Solution:

Total width=1 cm+9 cm=10 cm\text{Total width} = 1\text{ cm} + 9\text{ cm} = 10\text{ cm} Efficiency=1 cm10 cm×100=10%\text{Efficiency} = \frac{1\text{ cm}}{10\text{ cm}} \times 100 = 10 \%

Explanation:

Since the width of the arrows in a Sankey diagram is proportional to the energy, we can use the ratio of the useful arrow width to the total width to calculate efficiency. In this case, only 10%10\% of the energy is converted to light.

Problem 3:

A heater is 95%95 \% efficient. If it is supplied with 80008000 J of energy, how much energy is converted into useful thermal energy?

Solution:

Useful Energy=0.95×8000=7600 J\text{Useful Energy} = 0.95 \times 8000 = 7600 \text{ J}

Explanation:

To find the useful output, multiply the total input energy by the efficiency expressed as a decimal (95%=0.9595 \% = 0.95).