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Applications of Thermal Expansion in Solids (i) Bimetallic strip: If two strips of different metals are welded together to form a bimetallic strip, when heated uniformly it bends in the form ofan arc, the metal with greater coefficient of linear expansion lies on convex side. 0 At tc
At t1 c tiOc R. The radius of arc thus formed by bimetal is, or R where t temp. difference between the two ends. d-thickness of each strip oi and 2 are coefficients of linear expansion of two different metals.
(ii) Thermal stress in a rigidly fixed rod: Thermal strain- li 2 stress In elasticity, Young's modulus- Thermal stress-Y (t2-ti) Tensile strain ~aAt (iii) Effect of temperature on pcadulum clock: Change in time period, 7-T2-T,-- . .Ti 2
Expansion of liquic When a liquid is heated, its container also expands. The observed expansion of the liquid is called apparent expansion which is different from the real expansion of the liquid. Coefficient of apparent expansion. The coefficient of apparent expansion of the liquid is given by Apparent increase in volume Original volume x rise in temperature Coefficient of real expansion. The coefficient ofreal expansion of the liquid is given by Real increase in volume Yr Original volume x rise in temperature It can be proved that + g where Tg is coefficient ofcubical expansion ofglass (material) of the container
Change in Density with Temperature Suppose m is the mass of a solid which is at a given temperature occupies a volume V so that density at 0 C is do- Now, if the temperature is increased by t C, mass will remain unchanged but due to thermal expansion volume increases so that, V'-V(1 +yAt) Now density, d, - do(1 -ir) Here Yis coefficient of cubical expansion of the substance at 0C.
Anomalous Expansion of Water Almost all liquids expand on heating but water when heated from 0 C to 4 C its volume decreases and hence density increases until its temperature reaches 4 C. Its density is maximum at 4 C on further heating its density decreases. This behaviour of water is called anomalous behaviour of water.
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