Predict warming and cooling from unequal energy rates
Use signed net power and elapsed time before making a temperature claim.
Extended only (Supplement); Physics 0625, 2026–2028, section 2.3.3. These lessons cover steady and unequal rates, Earth radiation balance, emitter/absorber experiments and temperature/area effects. Written calculations and described methods are self-checked
Before you begin
- Balance complete energy-transfer rates.
- Distinguish fixed-state warming from phase change.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Input is 20 W and total outgoing is 35 W. What is the signed net rate?
What you will learn
- Predict warming or cooling when received and outgoing rates differ in a fixed-state account.
- Calculate net energy change while retaining all transfer routes and assumptions.
Find the signed net rate into the object
For a fixed-state positive-heat-capacity object with no other changing stores, receiving more energy per second than it transfers away raises its internal energy and temperature. Receiving less gives a loss and cooling. Define net rate into the object as total input minus total output, so a negative sign describes a loss from that boundary.
An input of 50 W and outputs totalling 35 W give +15 W net. If rates remain constant for 120 s, the gain is 1800 J. An input of 20 W with outputs 35 W gives −15 W and a −1800 J change over the same duration. These are supplied energy accounts; a temperature rise in degrees needs the object's thermal properties as well.
Do not omit a mechanism or predict forever
The outgoing radiation rate often changes as surface temperature changes, and other thermal routes may also vary. A constant-rate calculation is for the supplied interval, not a prediction of unlimited warming at the same rate. A later steady temperature can result when the complete rates become equal.
During a state change, a net energy gain can change phase without the same temperature rise. Other stores or internal sources also require the stated boundary to be expanded. Use the fixed-state assumption explicitly; an infrared-emission reading alone does not establish net warming or cooling when input and other outputs are unknown.
Pause and explain
A fixed-state object gains 1800 J, but mass and c are unknown. What can be stated?
Worked example
A fixed-state object receives 50 W, loses 35 W in total and keeps these rates for 120 s. Find its net energy change and qualitative response.
Show the worked solution
- Net rate is 50 − 35 = +15 W.
- ΔE = 15 × 120 = +1800 J.
- With the stated unchanged state and no other stores, its temperature rises; an exact rise is not determined here.
Answer +1800 J; warming under the stated fixed-state account.
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Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Find net energy change for 50 W input, 35 W total output and 120 s at constant rates.
Give me a hint
Use a signed net rate into the object.
Compare my reasoning
- Net rate is +15 W.
- Multiply by 120 s.
- The gain is +1800 J.
+1800 J.
Look for these in your work
- Use the full output.
- Retain the stated interval.
Find the signed change for 20 W input, 35 W output and 120 s, then describe a fixed-state response.
Give me a hint
Subtract output from input before multiplying.
Compare my reasoning
- Net rate is −15 W.
- ΔE = −15 × 120 = −1800 J.
- The fixed-state object loses internal energy and cools under the stated assumptions.
−1800 J; cooling in the supplied fixed-state account.
Look for these in your work
- Preserve the loss sign.
- State the qualitative assumption.
A surface emits 25 W by radiation. Can you determine whether it warms from that reading alone?
Give me a hint
Received energy and other outgoing routes are missing.
Compare my reasoning
- 25 W is only one outgoing rate.
- Input and other outputs are unknown.
- The signed complete net rate, and therefore the temperature trend, is not determined.
No; one emission rate alone does not determine net warming or cooling.
Look for these in your work
- Identify the missing rates.
- Avoid using emission as a net-change measurement.
Common mistakes
- Use input minus every output.
- A supplied constant rate is not an unlimited-time prediction.
- An exact temperature change needs thermal properties and state conditions.
What can you explain now?
What does a negative net rate into the object mean?
Compare with the explanation
It loses energy overall.
Outputs exceed inputs for that specified boundary and interval.
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Make it stick
Find signed net rates and explain why temperature trends and numerical rises need a complete fixed-state account.
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