“One, two, three”
Linear, area and volume expansion
α : β : γ = 1 : 2 : 3. One dimension, two dimensions, three dimensions, in that order.
Class 11 Physics · Gujarat Board, CBSE, GUJCET and JEE
Thermal Properties of Matter formulas
Heat and temperature are not the same thing, and this chapter exists to make that difference precise. Expansion, calorimetry and the three modes of heat transfer each bring a small formula set, and the radiation laws at the end carry marks in both the board and the entrance papers.
16 formulas, 3 memory hooks, and the 5 mistakes that cost the most marks.
Thermal expansion
| What | Formula | Symbols and notes |
|---|---|---|
| Linear expansion | ΔL = LαΔT | α is the coefficient of linear expansion, per °C |
| Area expansion | ΔA = AβΔT, β = 2α | for a flat sheet |
| Volume expansion | ΔV = VγΔT, γ = 3α | for solids; liquids have their own γ |
| Relation | α : β : γ = 1 : 2 : 3 | the single most asked line of this chapter |
| Thermal stress | σ = YαΔT | when a rod is held so that it cannot expand |
Calorimetry
| What | Formula | Symbols and notes |
|---|---|---|
| Heat and temperature change | Q = mcΔT | c is specific heat capacity, J kg−1 K−1 |
| Latent heat | Q = mL | during a change of state the temperature does not move |
| Latent heat of fusion of ice | Lf = 3.34 × 10⁵ J kg−1 | melting ice at 0 °C |
| Latent heat of vaporisation of water | Lv = 22.6 × 10⁵ J kg−1 | boiling water at 100 °C |
| Principle of calorimetry | heat lost = heat gained | in an insulated mixture |
Heat transfer
| What | Formula | Symbols and notes |
|---|---|---|
| Conduction | Q/t = kA(T₁ − T₂)/L | k is thermal conductivity; needs matter and no bulk motion |
| Thermal resistance | R = L/kA | resistances in series add, as in an electric circuit |
| Stefan-Boltzmann law | E = σeAT⁴ | σ = 5.67 × 10−8 W m−2 K−4, e is emissivity |
| Net radiation | Enet = σeA(T⁴ − T₀⁴) | T₀ is the surroundings' temperature |
| Wien's displacement law | λmT = 2.898 × 10−3 m K | hotter bodies glow at shorter wavelengths |
| Newton's law of cooling | dT/dt ∝ (T − T₀) | valid for a small temperature difference |
Taught by Darshit Bhatt, founder and lead faculty at Darshit Sir Institute. Instrumentation and Control engineer, with a master's degree and a chartered degree, teaching in Paldi, Ahmedabad since 2006.
Know the formula but not when to use it?
Darshit Sir has taught this in Paldi since 2006, in the classroom and live online.
Memory hooks
How to remember this chapter.
“Latent means hidden”
Why temperature stops during melting
During a change of state the heat goes into breaking bonds, not into raising temperature, so the thermometer does not move while ice melts.
“Fourth power punishes heat”
Stefan's law
Radiated power goes as T⁴, so doubling the absolute temperature multiplies the radiation by sixteen.
Where marks go
The mistakes that cost the most.
- Using °C in Stefan's law or Wien's law. Both need kelvin, because both use absolute temperature.
- Forgetting the latent heat step when ice at 0 °C becomes water at 0 °C. Q = mcΔT gives zero there, and mL is the whole answer.
- Mixing up specific heat capacity and heat capacity. Specific heat is per kilogram; heat capacity is for the whole body.
- Treating β as 3α. Area uses 2α; only volume uses 3α.
- Applying Newton's law of cooling to a large temperature difference, where it stops being accurate.
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