Tiêu đề THERMAL ENERGY.pdf ✅

CLASS VIII PHYSICS It has been experimentally found that the increase in length of a metal rod, on heating, is directly propor- tional to : (i) original length of the rod i.e., L2 − L1 ∝ L1 (ii) rise in temperature L2 − L1 ∝ T2 − T1 Combining (1) and (2), L2 − L1 ∝ L1 ( T2 − T1 ) L2 − L1 = αL1 ( T2 − T1 ) L2 = L1(1 + αΔT) (where, α is the coefficient of linear expansion) ➢ Coefficient of Linear expansion (α) ∶ The coefficient of linear expansion is defined as the increase in length per unit original length per degree rise in temperature. α = Increase in length original length × Rise in temperature α = L2 − L1 L1 ( T2 − T1 ) = ΔL L1(ΔT) ➢ Unit of coefficient of linear expansion : In CGS system, its unit is ∘C −1 In S.I system, its unit is K −1 In the similar sense let us define Coefficient of Areal expansion and Coefficient of Cubical expansion. ➢ Coefficient of Areal expansion: The coefficient of superficial expansion of a metal is defined as the increase in its area per unit original area per degree rise in temperature.$ i.e. β = A2 − A1 A1 (T2 − T1 ) = ΔA A1(ΔT) A2 − A1 = A1 × β × (T2 − T1 ) A2 = A1 × [1 + β(T2 − T1 )] A2 = A1(1 + βΔT) • Unit of Coefficient of Areal expansion : In CGS system, its unit is ∘C −1 In S.I system, its unit is K −1 Coefficient of Cubical (or Volume) Expansion : The coefficient of cubical expansion of a liquid is defined as the increase in volume per unit original volume per degree rise in the temperature.$ i.e. γ = V2 − V1 V1 ( T2 − T1 ) = ΔV V1(ΔT) ⇒ V2 − V1 = V1 × γ × (T2 − T1 ) ⇒ ΔV = V1 × γ × ΔT ➢ Relationship amongα, β and γ : The coefficient of linear expansion α, coefficient of superficial expansion β and coefficient of cubical expan- sion γ are related as follows :
CLASS VIII PHYSICS β = 2α and γ = 3α; i.e. γ 3 = β 2 = α 1 ⇒ α: β: γ = 1: 2: 3 THERMAL EXPANSION Relation between the three coefficient of expansion of a body : Consider a solid cube of each side L0. Let area A0 = L0 2 and Volume V0 = L0 3 be the surface area of each face of the cube. Let the temperature of the cube be raised by a small amount ΔT such that the length of each side becomes L. Area of each face will be A such that A = L 2 . Similarly volume of the cube will be V such that V = L 3 1) Relation between α and β ∶ We know that L = L0(1 + αΔT) − − − −(1) Squaring on both sides we get$ L 2 = L0 2 (1 + αΔT) 2 A = A0(1 + αΔT) 2 A = A0 (1 + 2αΔT + α 2ΔT 2 ) Since α is very small therefore the term α 2ΔT 2 can be neglected.$ \mathrm{A}=\mathrm{A}_0(1+2 \alpha \Delta \mathrm{T})-\cdots(2)$ Also A = A0(1 + βΔT) − − − − − (3) Comparing equations (2) and (3), We get β = 2α 2) Relation between α and γ ∶ By taking the cube of equation (1), we get$ L 3 = L0 3 (1 + αΔT) 3 V = V0 (1 + 3αΔT + 3α 2ΔT 2 + α 3ΔT 3 ) Since α is very small therefore the terms α 2ΔT 2 and α 3ΔT 3 can be neglected$ V = V0(1 + 3αΔT) V = V0(1 + γΔT) Comparingequations(5)and(6), weget Comparingequations(4)and(7)weget α: β: γ = α: 2α: 3α α: β: γ = 1: 2: 3 ➢ Different forms:- 1. α 1 = β 2 = γ 3 2. 6α = 3β = 2γ 3. β = 2α = 2 3 γ 4. γ = 3α = α + β 5. γ = 3α = 3 2 β ➢ Some important points:- ➢ For the same rise in temperature, percentage change in area = 2 × Percentage change in length. ➢ For the same rise in temperature, Percentage change in volume = 3 × Percentage change in length. SYNOPSIS - 2