Close an idealized energy balance

Supplied materials

• All measurements and observations below are supplied classroom examples. They are not data from actual learners or a claim about a particular real site.
• Paper or browser document; an ordinary calculator is optional.
• Rule: Net input equals incoming supplied energy minus outgoing supplied energy. Formula: a-b. Variable key: a = incoming energy (model units), b = outgoing energy (same units)
• Distinct worked inputs and result: A distinct model receives 210 units and loses 205: net +5 units accumulate over that interval.
• Assessment case 1: Supplied case 1: incoming energy (model units)=240; outgoing energy (same units)=230, using the explicitly named quantities. Net input equals incoming supplied energy minus outgoing supplied energy. What result follows?
• Assessment case 2: Supplied case 2: incoming energy (model units)=250; outgoing energy (same units)=245, using the explicitly named quantities. Net input equals incoming supplied energy minus outgoing supplied energy. What result follows?
• Assessment case 3: Supplied case 3: incoming energy (model units)=220; outgoing energy (same units)=225, using the explicitly named quantities. Net input equals incoming supplied energy minus outgoing supplied energy. What result follows?
• Assessment case 4: Supplied case 4: incoming energy (model units)=260; outgoing energy (same units)=250, using the explicitly named quantities. Net input equals incoming supplied energy minus outgoing supplied energy. What result follows?
• Assessment case 5: Supplied case 5: incoming energy (model units)=230; outgoing energy (same units)=228, using the explicitly named quantities. Net input equals incoming supplied energy minus outgoing supplied energy. What result follows?
• Assessment case 6: Supplied case 6: incoming energy (model units)=245; outgoing energy (same units)=248, using the explicitly named quantities. Net input equals incoming supplied energy minus outgoing supplied energy. What result follows?

Learn the idea

An energy balance compares incoming and outgoing transfers over the same boundary and interval. A positive imbalance means energy accumulates in this simplified system; it is not automatically an instantaneous temperature change.

Net input equals incoming supplied energy minus outgoing supplied energy. The formula in the supplied model is a-b. Variable key: a = incoming energy (model units), b = outgoing energy (same units). Use the same boundary and interval. Keep negative values when output exceeds input.

A distinct model receives 210 units and loses 205: net +5 units accumulate over that interval. Net input is not itself a temperature measurement. Track the quantity and unit before calculating. Explain the meaning of a positive, negative or fractional result when relevant. A numerical answer supports the stated model calculation; broader claims require the additional measurements and assumptions described here.

1. Name the measured quantities and their units before substituting values.
2. Write the stated rule and use the variable key to match each symbol to its explicitly named quantity.
3. Calculate each supplied case separately, keeping intermediate arithmetic and the result unit.
4. Explain the result in context and identify the assumption that would invalidate direct use of the rule.

Check your reasoning

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Take it further

Changed-input task: use the same stated model with incoming energy (model units)=241; outgoing energy (same units)=230. Expected result: 11 model energy units. Explain what changes and keep this assumption: Net input is not itself a temperature measurement.

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