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Kumar Rohan

Physics and Mathematics

Thermal Properties of Matter — Complete Formula

⭐ – Most used in JEE
⚠️ – Common Mistake
💡 – Memory Hint

Temperature & Heat

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Heat	[Q = mc\Delta T]	[Q] = heat, [m] = mass, [c] = specific heat, [\Delta T] = temperature change	J	Basic relation ⭐
Heat Capacity	[C = \dfrac{Q}{\Delta T}]	[C] = heat capacity	J/K	For whole body
Specific Heat	[c = \dfrac{Q}{m\Delta T}]	—	J/kg·K	Depends on material

💡 Memory Hint:
Heat required ∝ mass × temperature change

Thermal Expansion

Linear Expansion

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Change in Length	[\Delta L = \alpha L \Delta T]	[\alpha] = coefficient of linear expansion, [L] = original length	m	Most basic ⭐

Area Expansion

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Change in Area	[\Delta A = 2\alpha A \Delta T]	[A] = area	m²	Coefficient = [2\alpha]

Volume Expansion

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Change in Volume	[\Delta V = \gamma V \Delta T]	[\gamma] = volume coefficient	m³	[\gamma \approx 3\alpha] ⭐

💡 Memory Hint:
Linear : Area : Volume → 1 : 2 : 3

Anomalous Expansion of Water

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Maximum Density	Occurs at [4^\circ C]	—	—	Water behaves abnormally ⚠️

💡 Memory Hint:
Water is densest at 4°C

Calorimetry

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Heat Balance	[\text{Heat lost} = \text{Heat gained}]	—	—	No heat loss to surroundings ⭐
Mixing Formula	[m_1 c_1 (T_1 – T) = m_2 c_2 (T – T_2)]	[T] = final temperature	J	Very important ⭐

💡 Memory Hint:
Hot loses = Cold gains

Change of State (Latent Heat)

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Latent Heat	[Q = mL]	[L] = latent heat	J	No temperature change ⭐
Fusion	[Q = mL_f]	[L_f] = latent heat of fusion	J	Solid ↔ liquid
Vaporization	[Q = mL_v]	[L_v] = latent heat of vaporization	J	Liquid ↔ gas

💡 Memory Hint:
Phase change → temperature constant

Heat Transfer

Conduction

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Heat Flow	[Q = \dfrac{kA\Delta T}{L} \cdot t]	[k] = thermal conductivity, [A] = area, [L] = length, [t] = time	J	Fourier’s law ⭐

💡 Memory Hint:
More area → more heat flow

Radiation

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Stefan’s Law	[P = \sigma A T^4]	[\sigma] = Stefan constant	W	Very important ⭐
Net Radiation	[P = \sigma A (T_1^4 – T_2^4)]	—	W	Surroundings effect ⚠️

💡 Memory Hint:
Radiation ∝ T⁴

Newton’s Law of Cooling

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Cooling Law	[\dfrac{dT}{dt} \propto (T – T_s)]	[T_s] = surroundings temperature	—	Valid for small ΔT ⭐

💡 Memory Hint:
Faster cooling when temperature difference is high

Thermal Resistance

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Thermal Resistance	[R = \dfrac{L}{kA}]	—	K/W	Opposes heat flow
Series Combination	[R_{eq} = R_1 + R_2]	—	K/W	Like resistors ⭐
Parallel Combination	[\dfrac{1}{R_{eq}} = \dfrac{1}{R_1} + \dfrac{1}{R_2}]	—	K/W	Alternate path

💡 Memory Hint:
Heat flow ↔ electric current analogy

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