What are coefficients of linear, superficial and cubical expansion, and give their derivation.
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Increase in length per unit of the length, per degree Celsius rise in temperature is called Coefficient of Linear expansion. Increase in area per unit of the original area, per degree Celsius rise in temperature is called Coefficient of Superficial expansion. Increase in volume per unit of the original volume, per degree Celsius rise in temperature is called Coefficient of cubic expansion. Please refer to your text book for the derivations. Note: Please refer to your text book for the derivations. Let Vs and Vl be the volumes of the solid and liquid at temperature T, respectively. When the system is heated both the solid block and the liquid expand and the volume of both increase. Let the increase in volumes of solid and liquid be ΔVs and ΔVl, at temperature T + ΔT, respectively.
As the depth of the submerged portion of the block does not change, the change in volume of the liquid is the same as the change in volume of the solid.
i.e. ΔVl = ΔVs
ɣ Vl ΔT = 3α Vs ΔT
ɣ = 3α Vs / Vl
where ɣ is the coefficient of volume expansion of the liquid and α the coefficient of linear expansion of the solid. Here we have made use of the fact the the volume coefficient of the solid is approximately equal to thrice the coefficient of linear expansion of the solid.
As the depth of the submerged portion of the block does not change, the change in volume of the liquid is the same as the change in volume of the solid.
i.e. ΔVl = ΔVs
ɣ Vl ΔT = 3α Vs ΔT
ɣ = 3α Vs / Vl
where ɣ is the coefficient of volume expansion of the liquid and α the coefficient of linear expansion of the solid. Here we have made use of the fact the the volume coefficient of the solid is approximately equal to thrice the coefficient of linear expansion of the solid.
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