Thermal Properties of Matter - Class 11 Physics

Thermal Properties

Overview: Study of effects of heat on matter: expansion, specific heat, phase change, and heat transfer.

1. Temperature & Expansion

Temperature is a measure of hotness. SI unit: Kelvin (K).

T_C / 5 = (T_F - 32) / 9

Thermal Expansion

Linear: ΔL = α L ΔT
Area: ΔA = β A ΔT (β = 2α)
Volume: ΔV = γ V ΔT (γ = 3α)

Anomalous Expansion of Water: Water contracts from 0°C to 4°C. Density max at 4°C.

2. Calorimetry

Specific Heat (s)

Heat required to raise temp of unit mass by 1°C.

Q = msΔT

Water: s = 4186 J/kg K (Highest among common substances).

Latent Heat (L)

Heat required to change state at constant temperature.

Q = mL

Fusion (Ice-Water): L_f = 3.33 × 10⁵ J/kg
Vaporization (Water-Steam): L_v = 22.6 × 10⁵ J/kg

3. Heat Transfer Methods

Conduction

Heat transfer through solids without material movement.

H = KA (T₁ - T₂) / L

K is thermal conductivity.

Convection

Heat transfer in fluids by actual movement of matter (Sea Breeze, Trade winds).

Radiation

Transfer via Electromagnetic waves. No medium required.

E = σ A T⁴ (Stefan-Boltzmann Law)

Rate of cooling is proportional to temp difference (Newton's Law).

dθ/dt = - k (θ - θ₀)

4. Wien's Displacement Law

Wavelength of max emission is inversely proportional to Temperature.

λ_m T = constant (b)

b = 2.9 × 10^-3 mK. (Explains star colors).

Numericals - Thermal Properties of Matter

Numericals

Scale Conversion

Q1. At what temperature generally do Celsius and Fahrenheit scales read the same?

C/5 = (F-32)/9

Let C = F = x

x/5 = (x-32)/9

9x = 5x - 160

4x = -160 → x = -40

-40°C = -40°F

Linear Expansion

Q2. Brass rod of length 2m at 0°C. α = 18x10^-6 K^-1. Increase in length at 100°C?

ΔL = L α ΔT

ΔL = 2 × 18×10^-6 × 100

ΔL = 36 × 10^-4 m

ΔL = 3.6 mm

Volume Expansion

Q3. A 10 liter tank is full of petrol at 20°C. Car is left in sun at 40°C. How much overflows? (γ=950x10^-6)

ΔV = V γ ΔT

ΔV = 10 × 950×10^-6 × 20

ΔV = 190000 × 10^-6

ΔV = 0.19 Liters = 190 ml

Mixing (Calorimetry)

Q4. 100g water at 90°C mixed with 200g water at 30°C. Find final temp.

m1 s (T1 - T) = m2 s (T - T2)

100(90 - T) = 200(T - 30)

90 - T = 2T - 60

3T = 150 → T = 50°C

Latent Heat

Q5. Heat required to convert 10g ice at 0°C to water at 20°C? (L=336 J/g, s=4.2 J/gC)

Phase 1: Ice -> Water (mL)

Q1 = 10 × 336 = 3360 J

Phase 2: Heat water 0->20 (msΔT)

Q2 = 10 × 4.2 × 20 = 840 J

Total Q = 3360 + 840 = 4200 J

Heat Conduction

Q6. Rate of heat flow through a bar of K=200, A=0.01m², Length=0.5m, Temp diff=100°C.

H = KAΔT / L

H = 200 × 0.01 × 100 / 0.5

H = 200 / 0.5 = 400 J/s (Watts)

Newton's Law of Cooling

Q7. A body cools from 80°C to 50°C in 5 min. Surroundings at 20°C. Time to cool from 60°C to 30°C?

(T1-T2)/t = K [ (T1+T2)/2 - Ts ]

Case 1: (80-50)/5 = K [ 65 - 20 ]

6 = K(45) → K = 6/45 = 2/15

Case 2: (60-30)/t = (2/15) [ 45 - 20 ]

30/t = (2/15)(25) = 10/3

t = 9 minutes

Wien's Law

Q8. Max wavelength of sun is 500 nm. If another star has max wavelength 250 nm, find its Temp. (T_sun = 6000K)

λ T = constant

λ1 T1 = λ2 T2

500 × 6000 = 250 × T2

T2 = 2 × 6000 = 12000 K

Stefan's Law

Q9. If absolute temperature of a blackbody is doubled, how many times does radiated power increase?

E ∝ T⁴

E2 / E1 = (2T / T)⁴

Ratio = 2⁴ = 16

Power increases 16 times.

Ideal Gas P-T

Q10. Gas at 27°C and pressure P. Heated to 327°C at constant volume. New P?

P1/T1 = P2/T2 (Gay Lussac)

T1 = 300K, T2 = 600K

P/300 = P2/600

P2 = 2P

Formulas & Facts - Thermal Properties

Equations & Formulas

Concept	Formula
Fahrenheit to Celsius	F = (9/5)C + 32
Linear Expansion	ΔL = L α ΔT
Relation α β γ	α = β/2 = γ/3
Heat Capacity	Q = msΔT
Heat Conduction	H = KAΔT / L
Newton Cooling	dT/dt = -K (T - T_surr)
Stefan's Law	E = σ T⁴
Wien's Law	λ_m T = 2.9×10^-3
Ideal Gas Law	PV = nRT
Equivalent Conductivity	Series: L/K = L1/K1 + L2/K2

50 NEET Facts

Key points for Thermal Properties.

1. Heat vs Temp Heat is energy in transit. Temperature is measure of average kinetic energy of molecules.

2. Absolute Zero 0 Kelvin. Molecular motion ceases. -273.15 °C.

3. Triple Point Temp and Pressure at which solid, liquid, gas coexist. Water: 273.16 K, 0.006 atm.

4. Anomalous Expansion Water contracts on heating from 0 to 4 C. Saves aquatic life in frozen lakes.

5. Invar Alloy with very low α. Used in clocks.

6. Thermal Stress Developed if expansion is prevented. F = YAαΔT.

7. Bimetallic Strip Curves on heating. Metal with higher α is on convex side. Thermostats.

8. Specific Heat of Water Very high (4200 J/kgK). Used as coolant. Modulates climate.

9. Principal Specific Heats Gases have two: Cp and Cv. Cp - Cv = R (Mayer's relation).

10. Latent Heat of Steam Steam causes more severe burns than boiling water because it contains extra latent heat (540 cal/g).

11. Regelation Melting of ice under pressure and refreezing when pressure released. Making snowballs.

12. Boiling Point vs Pressure BP increases with pressure. Pressure cooker works on this.

13. Blackbody Perfect absorber and emitter of radiation. E.g., Lamp black (98%).

14. Kirchhoff's Law Good absorbers are good emitters. e = a.

15. Stefan's Law Total energy radiated per second per unit area E = σT⁴.

16. Cooling Curve Temp-Time graph. Slope decreases as temp difference decreases.

17. Greenhouse Effect Atmosphere traps infrared radiation re-emitted by Earth. Glass houses work similarly.

18. Sea Breeze Daytime: Land heats faster, air rises, cool air from sea flows in.

19. Thermos Flask Minimizes all 3 heat transfer modes. Vacuum (conduction/convection), Silvering (radiation).

20. Thermal Conductivity (K) Metals have high K (Free electrons). Wood/Air have low K.

21. Ingen Hausz Expt Ratio of thermal conductivities K1/K2 = L1² / L2² (Lengths of wax melted).

22. Phase Change Temperature remains constant during phase change (Melting/Boiling).

23. Evaporation Surface phenomenon. Causes cooling. Occurs at all temperatures.

24. Boiling Bulk phenomenon. Happens at specific BP.

25. Sublimation Solid directly to Gas. Camphor, Dry Ice.

26. Conductivity Units W m^-1 K^-1.

27. Solar Constant Energy received from Sun per unit area per second. S = 1360 W/m².

28. Pyrometer Measures high temp (Sun/Stars) based on radiation color (Wien's Law).

29. Newton's Law Limit Valid only for small temperature difference (< about 40 C).

30. Emissivity (e) Ratio of radiation emitted by body to blackbody at same T. 0 < e < 1. Blackbody e=1.

31. Thermal Resistance R = L / KA. Analogous to Electrical Resistance R = L / σA.

32. Series Combination Heat current H is same. R_eq = R1 + R2.

33. Parallel Combination Temp diff is same. 1/R_eq = 1/R1 + 1/R2.

34. Pendulum Clock Fast/Slow Summer (L increases) -> T increases -> Clock runs Slow. Winter -> Fast.

35. Holes in Plates Hole expands as if it were filled with the material. Radius increases on heating.

36. Density variation ρ' = ρ / (1 + γΔT). Density decreases on heating.

37. Apparent Expansion Liquids expand in a container. ΔV_app = ΔV_real - ΔV_container.

38. Water Equivalent Mass of water that absorbs same heat as body for same temp rise. W = ms.

39. Heat Capacity Total heat to raise body temp by 1K. H = Mass × Specific Heat.

40. State Functions P, V, T, U, S. Work and Heat are Path functions.

41. Color of Stars Red stars are cooler. Blue stars are hotter (Wien's Law).

42. Fraunhofer Lines Dark lines in solar spectrum. Absorption spectrum by elements in Sun's atmosphere.

43. Prevost Theory All bodies emit radiation at all temps > 0K. Rate depends on T.

44. Cooking in Hills Harder because BP of water is lower (due to low pressure). Pressure cooker essential.

45. Skating on Ice Pressure of skates melts ice into water (lubricant).

46. Woolen Clothes Trap air (bad conductor). Heat from body doesn't escape.

47. Mud Houses Cool in summer, warm in winter. Mud is bad conductor.

48. Cloudy Nights Warmer than clear nights. Clouds reflect earth's radiation back.

49. Thermocouple Measures temp based on Seebeck effect. Used for wide range (-200 to 1600 C).

50. Constant Volume Gas Thermometer Standard thermometer. Based on P ∝ T.

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