Temperature and Heat
Temperature: Measure of the average kinetic energy of molecules. SI unit: kelvin (K).
Heat: Form of energy transferred between bodies due to temperature difference. SI unit: joule (J).
Temperature Scales
| Scale | Freezing Point | Boiling Point | Relation |
|---|---|---|---|
| Celsius | 0 C | 100 C | C |
| Fahrenheit | 32 F | 212 F | F = 9C/5 + 32 |
| Kelvin | 273.15 K | 373.15 K | K = C + 273.15 |
Thermal Expansion
Linear Expansion
Delta L = alpha L_0 Delta T
alpha = coefficient of linear expansion (per C or per K).
Superficial (Area) Expansion
Delta A = beta A_0 Delta T
beta = coefficient of area expansion. beta = 2alpha.
Cubical (Volume) Expansion
Delta V = gamma V_0 Delta T
gamma = coefficient of volume expansion. gamma = 3alpha.
Anomalous Expansion of Water
Water contracts when heated from 0 C to 4 C. Density is maximum at 4 C. This allows aquatic life to survive under ice.
Thermal Stress
Stress induced when a material is prevented from expanding or contracting.
F/A = Y alpha Delta T
Applications: Gaps in railway tracks, expansion joints in bridges, bimetallic strip in thermostats.
Specific Heat
The amount of heat required to raise the temperature of a unit mass by 1 C (or 1 K).
Q = m c Delta T (where c is specific heat in J/kg K).
Molar Specific Heat
Heat required per mole per degree: C = Mc (where M is molar mass).
Specific Heat of Water
c_(water) = 4186 J/kg K. High specific heat makes water a good coolant.
Calorimetry
The measurement of heat transfer.
Principle of Calorimetry
Heat lost by hot bodies = Heat gained by cold bodies (in an isolated system).
m_1 c_1 (T_1 - T) = m_2 c_2 (T - T_2) where T is equilibrium temperature.
Calorimeter
A device used to measure heat transfer. Usually made of copper with a known specific heat.
Method of mixtures: Hot substance mixed with cold substance, equilibrium temperature measured.
Change of State
Latent Heat
Heat required to change the state of a substance without temperature change.
Latent Heat of Fusion (L_f): Solid to liquid. For ice: L_f = 3.36 x 10^5 J/kg.
Latent Heat of Vaporisation (L_v): Liquid to gas. For water: L_v = 22.6 x 10^5 J/kg.
Phase Diagram
Shows the state of a substance at different temperatures and pressures.
- Triple point: Temperature and pressure where all three phases coexist.
- Critical point: Beyond which liquid and vapour phases are indistinguishable.
Regelation
Ice melts under pressure and refreezes when pressure is released. Explains why ice skates slide easily.
Heat Transfer
Conduction
Transfer of heat through a material without bulk movement.
Q/t = k A (T_1 - T_2)/d (Fourier's law)
k = thermal conductivity (W/m K).
Thermal resistance: R = d/(kA).
Convection
Transfer of heat through fluid motion (bulk movement).
- Natural convection: Due to density differences (e.g., sea breeze).
- Forced convection: Using pumps/fans.
Radiation
Transfer of heat through electromagnetic waves. No medium required.
Stefan-Boltzmann Law: P = sigma A T^4
sigma = 5.67 x 10^(-8) W/m^2 K^4.
Newtons Law of Cooling: Rate of cooling is proportional to temperature difference.
(dT/dt) prop -(T - T_0).
Emissivity (e): Ratio of emissive power of a body to that of a blackbody. Perfect blackbody has e = 1.
Worked Examples
Example 1: A 1 m iron rod expands by 1.2 mm when heated from 20 C to 120 C. Find alpha.
Solution: alpha = Delta L/(L_0 Delta T) = 0.0012/(1*100) = 1.2 x 10^(-5) /C.
Example 2: 0.5 kg of water at 80 C is mixed with 0.3 kg of water at 20 C. Find equilibrium temperature.
Solution: 0.5*c*(80-T) = 0.3*c*(T-20) => 40 - 0.5T = 0.3T - 6 => 46 = 0.8T => T = 57.5 C.
Example 3: How much heat is needed to convert 1 kg of ice at -10 C to steam at 100 C?
Solution: Step 1: Ice -10 C to 0 C: Q_1 = 1*2100*10 = 21000 J.
Step 2: Ice to water at 0 C: Q_2 = 1*3.36x10^5 = 336000 J.
Step 3: Water 0 C to 100 C: Q_3 = 1*4200*100 = 420000 J.
Step 4: Water to steam: Q_4 = 1*22.6x10^5 = 2260000 J.
Total = 3037000 J.
Common Mistakes
- Unit of specific heat: J/kg K, not J/kg C (though numerically same due to same scale interval).
- Latent heat involves no temp change: Heat absorbed, but temperature remains constant.
- Specific heat vs heat capacity: Specific heat is per unit mass; heat capacity is for the whole body.
- Good conductors feel cold: They conduct heat away from your hand faster, making them feel colder.
ISC Exam Focus
- Theory (70%): Thermal expansion, specific heat, calorimetry principle, latent heat, heat transfer.
- Application (30%): Numerical problems on calorimetry, thermal expansion, heat transfer.
- ISC frequently asks calorimetry numericals with phase changes.
- Stefan-Boltzmann law and Newton's law of cooling are common.
Self-Test Questions
Q1: Convert 50 C to Fahrenheit and Kelvin.
Answer: F = 9*50/5 + 32 = 122 F. K = 50 + 273 = 323 K.
Q2: Find the final temperature when 0.2 kg of ice at 0 C is mixed with 0.5 kg of water at 40 C.
Answer: Heat to melt ice = 0.2*3.36x10^5 = 67200 J. Heat lost by water cooling to 0 C = 0.5*4200*40 = 84000 J. Excess heat warms resulting water: 84000 - 67200 = 16800 J. 16800 = (0.2+0.5)*4200*T => T = 5.71 C.
Q3: State Newton's law of cooling. Answer: Rate of cooling is directly proportional to temperature difference between body and surroundings.
Q4: Define coefficient of linear expansion and write its SI unit.
Answer: alpha = Delta L/(L_0 Delta T). Unit: /K or /C.
Q5: Why is water used as a coolant in car radiators? Answer: High specific heat (4186 J/kg K) allows water to absorb large amounts of heat with small temperature rise.
Q6: A metal rod of length 2 m at 30 C expands by 3 mm when heated to 130 C. Find alpha.
Answer: alpha = 0.003/(2*100) = 1.5 x 10^(-5) /C.
