Energy Conservation and Efficiency

What you’ll learn

Account for useful output and energy transferred elsewhere.

រាប់ថាមពលមានប្រយោជន៍ និងថាមពលផ្ទេរទៅកន្លែងផ្សេង។

Meaning and use

Energy is conserved when all transfers and stores are included. Useful output is the part serving the intended purpose; other transfers are often called wasted, though the energy is not destroyed. Efficiency compares useful output to input using the same units and interval.

ថាមពលរក្សានៅពេលរាប់ការផ្ទេរនិងស្តុកទាំងអស់។ ថាមពលដែលហៅថាខ្ជះខ្ជាយមិនបាត់បង់ពីធម្មជាតិទេ ប៉ុន្តែទៅជាកម្ដៅ ឬទម្រង់ផ្សេង។

Formulas

Energy accounting for the stated process

\[E_{\mathrm{in}}=E_{\mathrm{useful}}+E_{\mathrm{other}}\]

Efficiency

\[\eta=\frac{E_{\mathrm{useful}}}{E_{\mathrm{in}}}\times100\%\]

Symbols and units

Symbol	Meaning	Unit or restriction
Ein	Total energy input for the interval	J or another consistent energy unit
Euseful	Output serving the intended purpose	Same energy unit
Eother	Other transfers or accounted store changes	Same energy unit
η	Efficiency	Percent, from 0 to 100 in this simple accounting

Conditions and limits

• Include relevant stored-energy changes in the accounting.
• Use positive input and compare corresponding input and output over the same interval.
• កុំប្រៀបធៀប J នឹង kJ ដោយមិនបម្លែង។

Worked examples

A machine output

Input is 500 J; useful output is 300 J.

1. Efficiency \(\eta=(300/500)\times100\%=60\%\).
2. Other accounted energy \(500-300=200\) J.

60%; 200 J elsewhere

ថាមពលផ្សេងមិនត្រូវបានបំផ្លាញទេ។

Finding useful output

Input is 800 J and efficiency is 25%.

1. Use output \(=0.25\times800\).
2. Calculate 200 J useful output.

200 J

បម្លែង 25% ទៅ 0.25 មុនគុណ។

Common mistakes

Instead of	Use	Why
Wasted energy is destroyed.	It is transferred or stored in less useful forms.	Conservation includes the other transfers.
Efficiency = input / useful output.	Efficiency = useful output / input.	The useful share cannot exceed the properly accounted input in this model.

Practice

Solve these before revealing the worked solutions. Include units where relevant.

សាកល្បងដោះស្រាយមុនបើកមើលចម្លើយ។ សូមបង្ហាញជំហាន និងឯកតាដែលពាក់ព័ន្ធ។

1. Input 200 J, useful output 150 J: find efficiency.
2. Input 1000 J, efficiency 40%: find useful output.
3. A calculation gives 150% efficiency in this simple model. What should you check?

Answers and steps

Show solutions / បង្ហាញដំណោះស្រាយ

1. 75%

   150/200 × 100 = 75.

2. 400 J

   0.40 × 1000 = 400.

3. Units, omitted energy stores, and the input/output definitions.

   The stated accounting or measurements are inconsistent.

Quick recap

• Energy transferred elsewhere is not destroyed.
• Compare consistent units and intervals.
• Check the complete system boundary.