Thermal Expansion


\toWith the increase in temperature of a body, there is an increase in its dimension also. This property is known as thermal expansion. When temperature of body increases intermolecular separation also increases which result in thermal expansion of a body.\\\toWe can see thermal expansion in all states (liquid,gas and solid). Solids have all kinds of expansion but liquid and gases only have volume expansion.

Types of Expansion In Solids

  1. Increase in length of the body during heating.\\L_2=L_1(1+αLΔT), where L_1 and L_2 are the length before expansion and after expansion.\\α is coefficient of linear expansion, ΔT is change in temperature.\\Also, it can be represented by ΔL/L = αLΔT (ΔL = L_2-L_1)\\

  2. \textbf{Superficial Expansion: } \\Increase in Area of the body during heating.\\A_2=A_1(1+βAΔT), where A_1 and A_2 are the area before expansion and after expansion.\\β is coefficient of Superficial expansion, ΔT is change in temperature.\\Also, it can be represented by ΔA/A = βAΔT (ΔA = A_2-A_1)\\

  3. \textbf{Cubical Expansion: } \\Increase in Area of the body during heating.\\V_2=V_1(1+γ AΔT), where V_1 and V_2 are the area before expansion and after expansion.\\γ is coefficient of Cubical expansion, ΔT is change in temperature.\\Also, it can be represented by ΔV/V = γ VΔT (ΔV = V_2-V_1)\\

  4. \textbf{Notice:} \\The relation between α, β and ϒ α:β:ϒ = 1:2:3. α, β and ϒ solely depends only upon nature of material of body

Expansion of Liquid

  1. Liquids have only definite volume not definite shape. Its container determines its shape. When a liquid is heated in a vessel, both the liquid and a vessel expand.

  2. The change in volume of liquid relative to vessel is called its apparent expansion.\\

  3. The real change in volume of liquid only is called real expansion\\(without considering expansion of vessel). Thus there are two coefficients.\\Also, we can write: ϒ_r = ϒ_a + ϒ_v Where ϒ_r is the coefficient of real expansion, ϒ_a is the coefficient of apparent expansion of liquid, and ϒ_v is apparent expansion of vessel.

  4. The apparent change in volume of liquid is given by ∆V_a = V (ϒ - 3α)∆T.\\Where V is volume of liquid, ϒ is coefficient of volume expansion of liquid, α is coefficient of linear expansion of vessel.\\-If ϒ > 3 α, liquid level rises.\\-If ϒ < 3 α liquid level falls.\\-If ϒ = 3 α level of liquid remains stationary.

Temperature and Time Period

  1. Δt =\frac{1}{2}αΔT (Change in time period)\\

  2. (\frac{Δt}{t})*100=\frac{1}{2} αΔT (Percentage change in time period)\\Temperature increases → Loss in time period\\Temperature decreases → Gain in time period

Anomalous Expansion

  1. The anomalous expansion of water is an abnormal property of water\\whereby it expands instead of contracting when the temperature\\goes from 4^oC to 0^oC. Water has maximum density (volume minimum) at 4.\\

  2. The density becomes less and less as it freezes because molecules\\of water normally form open crystal structures when in solid form.

Bimetallic Strip

  1. A strip consisting of two metals of different coefficients of expansion\\welded together so that it buckles on heating.\\

  2. It is used as a thermostat and fire alarm.\\

  3. When bimetallic strip is cooled it bends towards larger coefficient of linear expansion.

Thermal Stress

  1. When a metal rod is heated or cooled it expands or contracts. If it is prevented from\\expansion or contraction, then stress produced is thermal stress.\\

  2. \textbf{Strain} =\frac{ΔL}{L}= α ∆T\\

  3. \textbf{Thermal stress } = Y x strain = Y α ∆T

  4. \textbf{Force} = stress x A = Y α ∆T x A\\

  5. ∴ \textbf{F} = YA α ∆T\\

  6. \textbf{Heating of Metal Plate with Hole}\\

  7. After expansion:\\R’ = R(1+α∆T) ….(i)\\r’ = r (1+α∆T) ….(ii)\\

  8. From (i) and (ii)\\

  9. R’.r=r’.R=constant

Memory Tips

  1. Two identical spheres (solid and hollow) are heated:\\i)By giving equal heat then hollow expand more as it has less mass.\\ii)By same temperature then both will expand equally.\\

  2. Two rods of length L_1 and L_2of linear expansivities α_1 & α_2 having\\same difference in temperature then L_1.α_1L_2.α_2 .\\

  3. Zeroth law of thermodynamics states that “If two bodies are thermal\\equilibrium separately with third body then these bodies are in thermal\\equilibrium with each other .”

Some More

  1. \toGases have only volume expansion.\\\toWhen temperature of liquid increases its volume increases and density decreases.\\\toAs density of substance decreases with increase in temperature so\\same volume of benzene weighs less in summer than in winter but same mass of\\benzene weighs equally in summer and winter (as mass is constant).\\\toWhen a metallic piece is weighed in a temperature increasing liquid then its apparent weight increases.\\\toInvar is used in pendulum clock (because of low coefficient of linear expansion.\\\toIf C and S are the coefficient of apparent expansion of copper and silver respectively. The coefficient of linear expansion of copper is A than silver is given by \frac{(C+3A-S)}{3}\\\toThe brass disc fits tightly in a hole in a steel plate. To lose the disc we should cool the system.\\\toThe correction in height of mercury level in barometer due to expansion of mercury is given by : H_{correct}=H_{scale}[1+( α –r)∆T]\\

  2. \toDensity decreases with increase in temperature ρ_tρ_0(1-r∆T)\\

  3. \toApparent expansion of vessel depends upon nature of liquid, orginal\\volume of liquid, change in temperature and material of vessel.\\\toReal expansion doesn’t depend on expansion of vessel but depends upon\\temperature difference of liquid, initial volume of liquid and its nature.\\\toWater will boil when a bottle of water at zero degree Celsius opened on\\surface of moon because pressure of air on the surface of moon is almost\\zero.

Thermal Expansion


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