Derivation refers to the process of deriving a formula or result from known principles or axioms. It involves mathematical manipulation such as differentiation integration or algebraic steps to obtain the desired equation. Derivation helps to explain and justify physical laws by using established concepts and principles of mathematics.
Chapter 10 of Class 11 Physics discusses thermal properties of matter focusing on concepts like temperature expansion of solids liquids and gases specific heat capacity heat transfer and thermal equilibrium. The chapter covers methods of measuring temperature such as thermometers and explains different laws related to heat energy transfer and change in state.
The coefficients of linear expansion (α), superficial expansion (β), and cubical expansion (γ) are interrelated based on the effect of temperature change on the length, area, and volume of a material.
1. Linear Expansion (α):
The change in length (ΔL) for a material due to temperature change is given by:
ΔL = α L ΔT
where α is the coefficient of linear expansion, L is the original length, and ΔT is the temperature change.
2. Superficial Expansion (β):
The change in area (ΔA) for a material due to temperature change is given by:
ΔA = β A ΔT
where β is the coefficient of superficial expansion, A is the original area, and ΔT is the temperature change.
Since area is related to length by A = L², the relation between β and α is:
β = 2α
3. Cubical Expansion (γ):
The change in volume (ΔV) for a material due to temperature change is given by:
ΔV = γ V ΔT
where γ is the coefficient of cubical expansion, V is the original volume, and ΔT is the temperature change.
Since volume is related to length by V = L³, the relation between γ and α is:
γ = 3α
4. Relation between α, β, and γ:
Combining the equations above:
β = 2α and γ = 3α
So the relation between three coefficients of expansion is,
β = 2α and γ = 3α
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