In general, bodies, whether solid, liquid or gaseous, increase in size as they increase in temperature.
A rise in temperature causes the vibration and distance between the atoms that make up a solid body to increase. As a result, an increase in their dimensions occurs.
Depending on the most significant expansion in a given dimension (length, width and depth), the expansion of solids is classified as: linear, superficial and volumetric.
Linear dilation takes into account the dilation suffered by a body in only one of its dimensions. This is the case, for example, with a thread, where its length is more relevant than its thickness,
To calculate linear dilation we use the following formula:
ΔL = L_{0}.α.Δθ
ΔL : Length Change (m or cm)
L_{0} _{: } Initial Length (m or cm)
α : Coefficient of linear expansion (ºC ^{ -1 })
Δθ : Temperature variation (ºC)
Surface swelling takes into account the swelling of a given surface. This is the case, for example, with a thin metal plate.
To calculate surface expansion we use the following formula:
ΔA = A_{0}.β.Δθ
ΔA : Area variation (m ^{ 2 } or cm ^{ 2 })
A _{ 0 }: Initial area (m ^{ 2 } or cm ^{ 2 })
β : Coefficient of surface expansion (ºC < sup> -1 )
Δθ : Temperature variation (° C)
It should be noted that the surface expansion coefficient (β) is equal to twice the value of the linear expansion coefficient (α), ie:
β = 2 . α
Volumetric dilation results from an increase in body volume, such as a gold bar.
To calculate volumetric dilation we use the following formula:
ΔV = V_{0}.γ.Δθ
ΔV : Volume change (m ^{ 3 } or cm ^{ 3 })
V _{ 0 }: Initial volume (m ^{ 3 } or cm ^{ 3 })
γ : Coefficient of volumetric expansion (ºC < sup> -1 )
Δθ : Temperature variation (° C)
Note that the volumetric expansion coefficient ( γ) is three times greater than the linear expansion coefficient (α), ie:
γ = 3 . α
The dilation a body undergoes depends on the material that composes it. Thus, in the calculation of the dilatation, the substance from which the material is made is taken into account through the linear expansion coefficient (α).
The table below indicates the different values that can assume the linear expansion coefficient for some substances:
Substância | Coeficiente de Dilatação Linear (ºC^{-1}) |
---|---|
Porcelana | 3.10^{-6} |
Vidro Comum | 8.10^{-6} |
Platina | 9.10^{-6} |
Aço | 11.10^{-6} |
Concreto | 12.10^{-6} |
Ferro | 12.10^{-6} |
Ouro | 15.10^{-6} |
Cobre | 17.10^{-6} |
Prata | 19.10^{-6} |
Alumínio | 22.10^{-6} |
Zinco | 26.10^{-6} |
Chumbo | 27.10^{-6} |
Os líquidos, salvo algumas exceções, aumentam de volume quando a sua temperatura aumenta, da mesma forma que os sólidos.
However, we must remember that liquids do not have their own form, acquiring the shape of the container that contains them.
Therefore, for liquids, it makes no sense to calculate either linear or superficial dilation, just volumetric.
Thus, we present below the table of the volumetric expansion coefficient of some substances.
Liquids | Volumetric Dilatation Coefficients (ºC ^{ -1 }) |
---|---|
Water | 1,3.10 ^{ -4 } |
Mercury | 1.8.10 ^{ -4 } |
Glycerin | 4,9.10 ^{ -4 } |
Alcohol | 11,2.10 ^{ -4 } |
Acetone | 14,93.10 ^{ -4 } |
Want to know more? Also read :
1) A steel wire is 20 m long when its temperature is 40 ° C. What will be its length when its temperature is 100 ° C? Consider the coefficient of linear expansion of steel equal to 11.10 ^{ -6 } ºC ^{ -1 }.
2) A square aluminum plate has equal sides at 3 m when its temperature is 80 ° C. What will be the variation in its area if the plate is subjected to a temperature of 100 ° C? Consider the linear expansion coefficient of aluminum 22.10 ^{ -6 } ºC ^{ -1 }.
3) One 250 ml glass bottle contains 240 ml of alcohol at a temperature of 40 ° C. At what temperature will alcohol begin to overflow from the bottle? Consider the coefficient of linear expansion of the glass equal to 8.10 ^{ -6 } ºC ^{ -1 } and the volumetric coefficient of alcohol 11,2.10 ^{ -4 } ºC < sup> -1 .