Explain steady temperature through balanced energy rates
Balance all input and output rates for a fixed-state object without claiming every transfer has stopped.
Section P2.3.3 · Radiation
Exam scope and assessment notes
Mapped to the named 0973 section using teaching from the corresponding single-science course. A 0973-specific review of every Core and Supplement objective is still in progress. Written practice is self-checked; it does not demonstrate supervised laboratory competence or award an official Cambridge grade. This qualification reports two grades on the 9–1 scale; confirm the entry route for your zone and exam series.
Before you begin
- Distinguish energy amounts from transfer rates.
- Identify the object boundary and all relevant transfers.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Input is 40 W and outputs are 25 W and 15 W. What is the net rate?
What you will learn
- Explain steady temperature using equal received and outgoing energy rates.
- Distinguish thermal steady state from zero individual transfers or a phase-change plateau.
Equal totals give zero net accumulation
For a fixed-mass object in an unchanged state with no other changing energy stores, a constant temperature requires its total received energy rate to equal its total rate of transfer away. Individual transfers can continue. The balance is between sums: radiation, convection, conduction and other specified inputs or outputs must be assigned to the same object boundary.
In a supplied account, an object receives 40 W and transfers away 25 W by radiation plus 15 W through other thermal routes. Total outgoing is 40 W, so the net rate is zero. Over 60 s, 2400 J enters and 2400 J leaves. Equal totals do not require each outgoing mechanism individually to equal the full input.
State the fixed-state assumption
A constant-temperature phase change is different: energy can change internal energy through melting or boiling while the temperature remains constant. Therefore a thermometer plateau alone is not proof of equal rates. This steady-object rule uses an unchanged state and no additional energy-store changes; retain those conditions rather than contradict the preceding phase-change lessons.
The diagram's arrows show named supplied rates, not measured universal values or proportional arrow widths. A complete account can establish steady state under its assumptions, while an incomplete account cannot prove that missing transfers vanish. The surface can still emit and absorb radiation at steady temperature.
Sources for this lesson
Pause and explain
Does constant temperature during melting prove balanced input and output?
Worked example
A fixed-state object receives 40 W and loses 25 W by radiation plus 15 W otherwise. Describe its temperature and the transfers over 60 s.
Show the worked solution
- Total outgoing rate is 25 + 15 = 40 W.
- Net rate is 40 − 40 = 0 W.
- Over 60 s, 2400 J enters and 2400 J leaves; steady temperature is supported under the stated fixed-state account.
Answer Steady temperature with continuing balanced transfers, not zero individual transfers.
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Test this topic →From guided practice to a new situation
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.
Balance a fixed-state object with input 40 W and outputs 25 W radiation and 15 W otherwise.
Give me a hint
Add all outputs before finding the net rate.
Compare my reasoning
- Outgoing total is 40 W.
- Input and outgoing rates are equal.
- The stated object can stay at steady temperature while each transfer continues.
Balanced rates support steady temperature under the supplied unchanged-state account.
Look for these in your work
- Include every output.
- Keep individual transfers continuing.
For the same account over 60 s, find received and outgoing energy amounts.
Give me a hint
Multiply each complete rate by duration.
Compare my reasoning
- Received energy is 40 × 60 = 2400 J.
- Outgoing total is (25 + 15) × 60 = 2400 J.
- Net change is zero under the stated complete boundary.
2400 J received and 2400 J transferred away.
Look for these in your work
- Distinguish joules from watts.
- Balance the same duration and boundary.
Ice melts at a constant reading while energy enters. Explain why this does not contradict the fixed-state balance rule.
Give me a hint
The phase and internal-energy conditions have changed.
Compare my reasoning
- The material changes state.
- Energy can increase internal energy without raising temperature during that change.
- The unchanged-state rule does not apply to the plateau as though melting were absent.
A phase change can gain energy at constant temperature; it is not the fixed-state case.
Look for these in your work
- Name the excluded condition.
- Preserve conservation.
Common mistakes
- Balance total rates rather than one route alone.
- Steady temperature can coexist with continuing transfers.
- A phase-change plateau is outside the unchanged-state inference.
What can you explain now?
Does a steady object have to stop emitting infrared?
Compare with the explanation
No.
It can continue emitting while received and total outgoing rates balance.
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Make it stick
Balance all rates for an unchanged-state object and distinguish this from a phase-change plateau.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.