PHYSICS (EXPANSION IN SOLIDS AND LIQUIDS)

SECOND TERM: WEEK 3

TOPIC: -                EXPANSION IN SOLIDS AND LIQUID

INSTRUCTIONAL MATERIALS: -                 

REFERENCES BOOK: -                                       

1.       FARINDE O. E e tal, ESSENTIAL PHYSICS FOR SSS, Tonad Publishing Limited.

2.       M. W. ANYAKOHA (2011), NEW SCHOOL PHYSICS FOR SENIOR SECONDARY SCHOOLS, Africana first publishers.  

3.       INTERNET

PREVIOUS KNOWLEDGE: - The Students have been familiar with thermometer.

INSTRUCTIONAL OBJECTIVES: -      At the end of the lessons students should be able to: -

1.       Define linear expansivity

2.       Solve problems on linear expansivity

3.       State Area and volume expansivity

4.       Solve mathematical problems related to area and volume expansivity.

5.       List some application of expansion.

CONTENT: -

EXPANSION IN SOLIDS AND LIQUID

Expansion and Contraction of Solids

When solids are heated they expand (increase in size/volume) and when cooled they contract (decrease in size/volume). Mass of the solid does not change when it contracts or expands.

Density of the solid increases when the body is cooled (because volume decreases) and it decreases when the body is heated (because volume increases).

Linear Expansivity.

Linear expansivity α of a substance is defined as the increase in length per unit length per degree rise in temperature.

α  =   =  ; where α = linear expansivity; l1 = length of metal at temperature , l2 = length of metal at temperature ;  θ= temperature rise which is given by

α  =   ; the unit of α is per K (K-1)

Linear expansivity is the tendency of a material to expand when heated. Different materials have different linear expansivities meaning that their rates of expansion or contraction are not the same except a few materials.

The unit of linear expansivity is measured in per Kelvin. The following are some examples;

Material                                                               Linear Expansivity (K-1)

Aluminum                                                                           26 x10-6

Brass                                                                                     19x10-6

Copper                                                                                                16.8x10-6

Iron                                                                                        12x10-6

Concrete                                                                             11x10-6

Steel                                                                                      11x10

Example

1(a)  What is meant by the statement: Linear expansivity of a solid is 1.0x10-5 K-1

  (b) Steel bars each of length 3m at 39oC are used for constructing a rail line. If the linear expansivity of the steel is1.0x10-5 K-1 . Calculate the safety gap that must be left between successive bars if the highest temperature expected is 41oC.

Solution

(a)    The solid will expand by 1.0x10-5 K-1 of its unit length for 1 K 0r 1 oC rise in temperature.

(b)   ɅL = L1αɅθ

α  = 1.0x10-5 K-1   ; Ʌθ = 41-39 = 2K;             L1 = 3m

ɅL = 1.0x10-5 K-1 x 3m x 2K = 6x10-6 m (safety gap)

2. Find the original length of a materials of linear expansivity of 1.0x10-6 K-1, at a temperature 20oC, it was later heated at a temperature of 72oC and increase the length to 18m.

Solution

α  = 1.0x10-6 K-1; θ1 =20 ; θ2= 72; L2 = 18m; L1= ?

α  =  ; 1.0x10-6 K-1 X L1(72-20) = 18 – L1; 0.000052L1 = 18 – L1;  L1 = 17.999m

AREA AND VOLUME EXPANSIVITY

  When a solid is heated, it increase in size, this is reffered to as Area of Superficial expansivity but when the object increases in volume, it then reffered to as volume or cubic expansivity.

Area expansivity (β) =  =

Example

Calculate the temperature changes due to a solid substance heated and area increases from 9cm2 to 9.02cm2 [Linear expansivity α = 1.4x10-6K-1]

Solution

A1= 9.00cm2; A2= 9.02cm2; α = 1.4x10-6K-1; β = 2x1.4x10-6K-1

 Β=  

 =  = 793.7K

volume expansivity (ϒ) =  =

CUBIC EXPANSIVITY OF A LIQUID SUBSTANCE

This is to relate the real and apparent cubic expansivity of a liquid.

Real cubic expansivity of a liquid can be defined as the increase in volume per unit volume per degree rise in temperature represented as ϒr.

Apparent cubic expansivity of a liquid can be defined as increase in volume per unit volume per degree rise in temperature when the liquid is heated in an expansible vessel ϒa.

ϒ = ϒr – ϒa i.e different in apparent and real expansivity is cubic expansivity of the container.

Real expansion = Apparent expansion + expansion of the container

ϒa =  =

VARIATION OF DENSITY WITH TEMPERATURE

Density =  ; ρ =

V2 = V1 (1+ϒθ)

V2 =  ;  V1 =

 =    (1+ϒθ);    ρ1m = ρ2m ((1+ϒθ);  ρ1 = ρ2 ((1+ϒθ)

Where ρ1=density at lower temperature;  ρ2 = density at higher temperature.

Example

A density bottle hold 300g of liquid at 25oC and 250g at 75oC. Calculate (a) apparent cubic expansivity (b) the real cubic expansivity of the liquid. If the linear expansivity of the material bottle is 0.000006K-1.

Solution

(a) ϒa =  = ;      ϒa =  =  =  = 0.004K-1

(b) ϒ = 3 α = 3 x 0.000006 = 1.8x10-5K-1

APPLICATION OF EXPANSION

Expansion is applied in the following area:

1.       Expansion in building and steel bridge.

2.       Railing lines

3.       Sagging of the telephone wires.

4.       Bimetallic strip e.g balance wheel of clock and watches, thermometer

5.       Expansion of glass

PRESENTATION

Step 1: The teacher introduces the new topic to the student

Step 2: The teacher leads the students to solve mathematical problem on linear expansion

Step 3: The teacher explains area and volume expansivity.

Step 4: The teacher guides the students to solve problems on area and volume expansivity

Step 5: The teacher explain the application of expansion.

EVALUATION

The teacher assesses the students with these questions:

1.       Define linear expansivity

2.       Solve problems on linear expansivity

3.       State Area and volume expansivity

4.       Solve mathematical problems related to area and volume expansivity.

5.       List some application of expansion.

ASSIGNMENT

1.       A brass measuring tape is correct at 20oC. The value obtained when the length of the field is measured with the rule at 50oC appears to be 70.5m. what is the true length of the field? Linear expansivity of brass = 1.8x10-5K-1. [ans-70.46m]

2.       A glass bottle full of mercury has mass 500g. on being heated through 35oC, 2.43g of mercury are expelled. Calculate the mass of mercury remaining in the bottle.[Cubic expansivity of mercury is 1.8x10-4K-1; linear expansivity of glass is 8.0x10-6K-1] (ans-445.05g)

 

 

 

  

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