Key relationship
T(t)=Ta+(T₀−Ta)e^(−kt); dT/dt=−k(T−Ta).
Physics · Class 11
Track cooling toward ambient
Newton cooling makes the rate proportional to the current temperature difference. Cooling is fastest initially and slows as the body approaches ambient. If initially colder, the same law predicts warming.
Open the interactive experiment →Track cooling toward ambient
நியூட்டன் குளிர்வு விதியில் வெப்பநிலை மாற்ற வீதம் சுற்றுப்புறத்துடனான வெப்பநிலை வேறுபாட்டிற்கு நேர்விகிதம்.
Key notes, relationships and model limits
Remember
Newton cooling makes the rate proportional to the current temperature difference. Cooling is fastest initially and slows as the body approaches ambient. If initially colder, the same law predicts warming.
Common trap
Constant surroundings do not produce a constant cooling rate.
Model limits
Lumped body with uniform temperature and constant surroundings. Newton cooling is an approximation over a suitable temperature range; constant k excludes changing convection and strong radiation.
What you will learn
Read exponential approach and distinguish rate from temperature difference.
Try the experiment
Try both scenarios, change one control, and predict the result before checking the graph and readouts.
Think of it this way
Change one input while keeping the others fixed, as you would in a controlled experiment.
Worked example
After 5 s, T=20+80e⁻¹=49.43°C. The body then cools at only −5.886 K/s.
Why this matters
The model connects track cooling toward ambient with an observable reading. Check the equation and assumptions before applying it.
Before you start
SI units · algebra · graph reading
Check your understanding
At T=100°C, Ta=20°C and k=0.2/s, what is the initial cooling rate?
- −20 K/s
- −16 K/s
- +16 K/s
Read the explanation
dT/dt=−0.2×(100−20)=−16 K/s.
Course connection: Class XI Chapter 10. Consult the roadmap for CBSE, NEET, JEE Main and Advanced scope.