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The effect of heat on matter:Linear, cubic, and superficial expansion

The effect heat


The effect of heat on matter:Linear, cubic, and superficial expansion

   The effect of heat energy on matter

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

  1. 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.
  2. Cracking noise in the building: the cracking noise heard from building result from expansion or contraction of galvanized iron sheet used in the roofing.
  3. 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

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

\alpha =\frac { L2-l1 }{ L2(\theta 2-\theta 1) } k{  }^{ -1 }

Where  l2 , l1 are final and initial length respectively, Ѳ21 are final and initial temperature respectively.

Example: A brass of length 100m increase to 100.5m when heated from 50oc to 100oc. Calculate its linear expansivity (α)

Solution: Ѳ2=100oc, Ѳ1 = 50oc, l2 = 100.5m, l1 =100m

Using  \alpha =\frac { L2-l1 }{ L2(\theta 2-\theta 1) } k{  }^{ -1 }

\frac { 0.5 }{ 100\times 50 } =10^4k{  }^{ -1 }

Example2: An iron of α =12 x 10-6k-1 and l1 = 60m, expands when heated through 100oc. Calculate (a) Increase in length. (b) Final length.

Solution, using

\alpha =\frac { L2-l1 }{ L2(\theta 2-\theta 1) } k{  }^{ -1 }

Ѳ2 –Ѳ1 =Ѳ, then l2-l1 = αL1Ѳ

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

(b) L2 = L1(1 + αѲ ) =60 (1 + 12 x 10-6 x 102 = 60.072

Area  or supercial expansivity:  it is written as

\beta =\frac { A2-A1 }{ A1\left( \theta 2-\theta 1 \right) }

Let Ѳ2 –Ѳ1 =Ѳ therefore   A2 –A1 = A1βѲ

A2 = A1(1 + βѲ)

Note A2, A1 are final and initial areas

Cubic or volume   expansivity:  is given by

\gamma =\frac { V2-V1 }{ V1\left( \theta 2-\theta 1 \right) }

Therefore V2 – V1 =v1γѲ

V2 = v1(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 25m2 ,  calculate

  • The increase in area, if it is heated through 40o
  • 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


\beta =\frac { A2-A1 }{ A1\theta }

Then  A2 –A1 = A1βѲ = 30 x 10-5 x 25 x 40 = 0.30m

Therefore A2 –A1 = increase in area = 0.30m2

For (b)

γ = 3α =3 x 15 x 10-5 =0.45 x 10-3k-1

Therefore      γ  = 0.45 x 10-3k-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  (γr)    of a liquid is the increase in volume per unit volume per rise in temperature .

Apparent cubic or volume expansivity ( γa) 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


Where γa = 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 10-5cm2.


  • the apparent increase in the volume  of the mercury when the temperature rises per
  • the distance between the fixed point (γ = 12 x 10-6oc-1)


\gamma =\frac { v2-v1 }{ v1(\theta 2-\theta 1)) }

V2 – v1  = γaV12 –Ѳ1)

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

h=\frac { 0.00048 }{ 0.0002 } =2.4cm

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 100oc

Assuming the expansivity of the container is 0.001oc. calculate the real expansivity

Solution (i)

\gamma {  }_{ a }\quad =\quad \frac { V2-V1 }{ V1(\theta 2-\theta 1) } \quad =\quad \frac { 0.05 }{ 10\times 100\quad  }

=5 x 10-5c-1

(ii)  γra

= 5 x 10-5 + 0.001

=1.05 x 10-3 oc-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


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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