Physics by Lamhi: Not Your Boring Physics

CLASS 11 · CHAPTER 10 · HEAT

QUICK REVISION

Thermal Properties of Matter

Every key result from this chapter, boxed and ready for a last look before the exam. No derivations here, just what to recall and when to use it — for the full explanation, see the detailed notes.

1. Temperature Scales

T(K)=T(∘C)+273.15,T(∘F)=95T(∘C)+32T(\text{K}) = T(^\circ\text{C}) + 273.15, \qquad T(^\circ\text{F}) = \dfrac{9}{5}T(^\circ\text{C}) + 32

2. Thermal Expansion

ΔL=L α ΔT,ΔA=A β ΔT,ΔV=V γ ΔT\Delta L = L\,\alpha\,\Delta T, \qquad \Delta A = A\,\beta\,\Delta T, \qquad \Delta V = V\,\gamma\,\Delta T
Expansion coefficient ratio (isotropic solid)
α:β:γ  ≈  1:2:3\alpha : \beta : \gamma \;\approx\; 1 : 2 : 3

3. Calorimetry

Specific heat
ΔQ=m c ΔT\Delta Q = m\,c\,\Delta T

Molar specific heat C=McC = Mc. Water: cwater=4186 J/(kg⋅K)c_{\text{water}} = 4186\text{ J/(kg·K)}.

Principle of calorimetry
Heat lost by hot body=Heat gained by cold body\text{Heat lost by hot body} = \text{Heat gained by cold body}

Insulated mixture, no heat escapes to surroundings.

4. Change of State and Latent Heat

Q=mLQ = mL

For water at 1 atm: Lf=333 kJ/kgL_f = 333\text{ kJ/kg} (fusion, at 0°C), Lv=2260 kJ/kgL_v = 2260\text{ kJ/kg} (vaporisation, at 100°C).

  1. Melting plateau (0°C): temperature flat — all heat breaks bonds, none raises KE.
  2. Boiling plateau (100°C): flat again, but far WIDER than the melting plateau — Qboil/Qmelt=2260/333≈6.8Q_{\text{boil}}/Q_{\text{melt}} = 2260/333 \approx 6.8 for the same mass.

5. Conduction

Steady-state conduction
dQdt=kA(T1−T2)x\dfrac{dQ}{dt} = \dfrac{kA(T_1-T_2)}{x}

kk = thermal conductivity, W/(m·K). Thermal resistance R=x/(kA)R = x/(kA), so dQ/dt=ΔT/RdQ/dt = \Delta T/R (Ohm’s-law analogy).

Series slabs
Req=R1+R2=x1k1A+x2k2AR_{\text{eq}} = R_1 + R_2 = \dfrac{x_1}{k_1A} + \dfrac{x_2}{k_2A}

6. Convection

  1. Natural convection: heated fluid expands, rises; cooler fluid sinks — sets up its own circulating current (land/sea breeze, boiling pot, weather).
  2. Forced convection: fluid pushed mechanically (fan, pump) — car radiator, blood circulation.

7. Radiation

Stefan–Boltzmann law (black body)
E=σAT4E = \sigma A T^4

σ=5.67×10−8 W/(m2K4)\sigma = 5.67\times10^{-8}\text{ W/(m}^2\text{K}^4). Doubling absolute temperature multiplies radiated power by 16.

8. Newton's Law of Cooling

Newton's law of cooling
−dTdt=k (T−T0)-\dfrac{dT}{dt} = k\,(T - T_0)

Linear approximation of radiative loss, valid only for small excess over surroundings T0T_0. For large excess, true T4T^4 behaviour makes cooling faster than this predicts.

Full derivations and worked examples: detailed notes →