Thermal expansion of solid: Solid expands when heated and contract when cooled. The rate of expansion of solid depends on the type of material the solid is made of. For example the rate of expansion of brass is difference from that of iron etc

Effect of expansion

Rail way lines and bridges: For example, it is because of thermal expansion that gaps are left in between the section of rail on rail way lines. If gap is not left in between the line, it may bend or crack during expansion.

Cracking noise in the building: the cracking noise heard from building result from expansion or contraction of galvanized iron sheet used in the roofing.

In telegram wire: During hot weather the metal used in constructing this wire expand and sag, while during cold weather they contract , so to give room for this effect , the wire are originally given some allowance to allow for the expansion as well as contraction.

Applications of thermal expansions

(i). it is used in removing tight stopper of glass bottle without cracking either the bottle or stopper

(ii). It is applied in productions of bimetallic strip, which in turn is used produce thermostat and strip thermometer.

Bimetallic strip: It consists of two difference metal like iron and brass which have difference expansion rate, joined together. When this metallic strip is heated, it bends due to difference in expansion of the brass and iron.

Bimetallic strip thermometer: this is made of coiled bimetallic spiral strip. The inside metal is usually made of invar or steel that hardly expand, while the outside is made of brass. One end of the spiral is fixed while the other end is attached spindle of the pointer. As the temperature increase the brass expands faster than invar. This difference in expansion allows the strip to curve inward making the pointer to move over a calibrated scale.

Use of thermostat in laundry iron: the thermostat which is made using bimetallic strip controls the temperature of electric laundry iron. When the iron reach a desire temperature mark, the thermostat will off the iron by curving away from what connected the current to the laundry iron, but when the iron cools, the thermostat straighten again and reconnect the iron to the current.

Types of expansion

Linear expansivity of solid α : it is defined as increase in length per unit length per a unit rise in temperature. That is

Where l_{2} , l_{1} are final and initial length respectively, Ѳ_{2},Ѳ_{1} are final and initial temperature respectively.

Example: A brass of length 100m increase to 100.5m when heated from 50^{o}c to 100^{o}c. Calculate its linear expansivity (α)

Example2: An iron of α =12 x 10^{-6}k-^{1} and l_{1} = 60m, expands when heated through 100^{o}c. Calculate (a) Increase in length. (b) Final length.

Solution, using

Ѳ_{2} –Ѳ_{1} =Ѳ, then l_{2}-l_{1} = αL_{1}Ѳ

= 12 x 10-6 x 60 x 100n= 0.72m

(b) L_{2} = L_{1}(1 + αѲ ) =60 (1 + 12 x 10^{-6} x 102 = 60.072

Area or supercial expansivity: it is written as

Let Ѳ_{2} –Ѳ_{1} =Ѳ therefore A_{2} –A_{1} = A_{1}βѲ

A_{2} = A_{1}(1 + βѲ)

Note A_{2}, A_{1} are final and initial areas

Cubic or volume expansivity: is given by

Therefore V_{2} – V_{1} =v_{1}γѲ

V_{2} = v_{1}(1 = γѲ)

Note that

β = 2α and

γ =3

Example: the linear expansivity of a material is 15 x10-5k^{-1}. If the initial area is 25m^{2} , calculate

The increase in area, if it is heated through 40^{o}

B cubic expansivity

Solution, using

Β = 2α but α = 15 x 10^{-5}

Therefore β = 2x 15 x 10-^{5} = 30 x 10-^{5}

Β =30 x 10-^{5}

using

Then A_{2} –A_{1} = A1βѲ = 30 x 10^{-5} x 25 x 40 = 0.30m

Therefore A_{2 }–A_{1} = increase in area = 0.30m^{2}

For (b)

γ = 3α =3 x 15 x 10-^{5} =0.45 x 10^{-3}k^{-1}

Therefore γ = 0.45 x 10^{-3}k^{-1}

Volume or cubic expansivity of a liquid:

Because liquid has no length or volume of its own, we only consider volume they take up with container.

Therefore in this context we talk of real (absolute) and apparent expansivity of liquids.

Real (absolute) cubic or volume expansivity (γ_{r}) of a liquid is the increase in volume per unit volume per rise in temperature .

Apparent cubic or volume expansivity ( γ_{a}) of a liquid is the increase in volume per unit volume for a unit rise in temperature when the liquid is heated in a expansible vessel .

The real expansivity is greater than the apparent because in apparent expansivity the expansion of the container has to be taken into account

γ_{r} =γ_{a }+γ

Where γ_{a }= apparent expansivity

Γ = cubic expansivity of of material containing the liquid.

Example; A mercury in-glass thermometer has bulb of volume 0.4cm and tube of area 20 x 10-5cm^{2}.

Calculate

the apparent increase in the volume of the mercury when the temperature rises per

the distance between the fixed point (γ = 12 x 10^{-6}oc-^{1})

Solution

V_{2 }– v_{1} = γ_{a}V_{1} (Ѳ_{2} –Ѳ_{1})

V2 –V1 =12 x 10-^{6} x 0.4 x 100 = 48 x 10^{-5}

For (b)

Let the Volume of the tube

= 20 x 10^{-5} x h = 48 x 10^{-5}

0.0002h = 0.00048

Example 2

(i) calculate the apparent expancivity of a liquid whose increase in volume is 0.05m3 and original volume is 100cm3, if it is raised through a temperature of 100^{o}c

Assuming the expansivity of the container is 0.001^{o}c. calculate the real expansivity

Solution (i)

=5 x 10-^{5}c^{-1}

(ii) γ_{r} =γ_{a} =γ

= 5 x 10-^{5} + 0.001

=1.05 x 10-^{3 o}c^{-1}

Change of state

There are three state of matter these include, solid, liquid and gas. For example when heat is applied to ice, it melts to liquid and when heat is also applied to liquid, it changes to gas through evaporation that is

ICE => LIQUID => GAS

Note that, the ice changing from solid state to liquid state without changing in temperature when heat is applied is called fusion of ice , the heat absorbed by a solid substance in changing from solid to liquid is latent heat of fusion

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