Lesson Notes By Weeks and Term - Senior Secondary School 1

SUBJECT: PHYSICS

CLASS:  SS 1

DATE:

TERM: 2nd TERM

REFERENCE BOOK

• New School Physics By M.W Anyakoha
• Senior Secondary School Physics By P.N Okeke

 
WEEK FOUR

TOPIC: Expansivity and Its Application - Linear, Area and Volume. Anomalous

Expansion of Water. Real and Apparent Expansivity

CONTENT

• Linear Expansivity of Solid

• Area Expansivity of Solid

• Cubic Expansivity of solid and Liquid

• Anomalous Behavior of Water

Linear Expansivity

Linear expansivity of a solid can be defined as increase in length per unit length, per unit degree rise in temperature. It is denoted by (α) and measure in per Kelvin or per degree Celsius. 

Mathematical representation

    α=     L2 – L1   

            L1 (Ó¨2 - Ó¨1)  ______________ (i)

Linear expansivity (α)= increase in length                           

                Unit length x temp change

L1 is the original length             Ó¨1 is the initial temperature

L2 is the final length                Ó¨2 is the final temperature

▲L = L2 – L1

▲Ө = Ó¨2 - Ó¨1                                                 α = ▲L              

                                                                                L1 ▲Ө        ________ (ii)

α = L2 – L1       

      L1 X ▲Ө

L2 – L1 = α L1 ▲Ө

L2 = L1 + X L1 ▲Ө  

L2 = L1 (1 + X ▲Ө)

N.B. ▲L = L2 – L1

         â–²Ó¨ = Ó¨2 - Ó¨1

1. A brass rod is 2m long at a certain temperature. What will be the length for a temperature rise of 100K , if the linear expansivity of brass 18 x 10-6K-1

SOLUTION

L1 = 2m,      L2 =?,     ▲Ө = 100K,     α = 18x1o-6k-1 

L2 = L1 (1 + α▲Ө)

L2 = 2 (1 + (18 X 10-6 X 100)

= 2(1 + 0.00018

= 2 (1.OOO18)

= 2.0036m

Area Expansivity

The area/superficial expansivity is the increase in area of per unit area per degree rise in temperature. It is donated by (β) and measured in per Kelvin and per 8C

β =     A2 – A1                  

              A1 (Ó¨2 - Ó¨1)

Recall; L2 = L1 (1 + α ▲ Ó¨)

Similarly b2 = b1 (1 + α ▲ Ó¨)

A2 = L1 (1 + α ▲ Ó¨) X b1 (1 + α ▲ Ó¨)

     = L1b1 (1 + α ▲ Ó¨) (1 + α ▲ Ó¨)

A2 = A1 (1 + 2 α ▲ Ó¨ + (α ▲Ө) ²

A2 = A1 (1 + 2 α ▲ Ó¨)

A2 = A1 (1 + β ▲ Ó¨)

EVALUATION

1. A brass rod is 2m long at a certain temperature. What will be its length for a temperature rise of 90K, if the linear expansivity of brass is 1.8 x 10-6K-1
2. Prove that A2 = A1(1 + β▲ Ó¨).

Volume/Cubic Expansivity

It is denoted by (Y). It is the increase in volume per unit volume per degree rise in 

temperature

Y = V2 – V1          

       V1 (Ó¨2 - Ó¨1)           ___________ (i)

Y = 3α _________ (ii)

Relationship between α: β: Y: = 1: 2

Real and Apparent Cubic Expansivity of Water

Real or absolute cubic expansivity (Yr) .The real / absolute of the liquid is the increase in volume by unit volume per degree rise in temperature.

Apparent Cubic Expansivity (Ya)

The apparent cubic expansivity is the increase in volume per unit rise when heated in an expansible vessel.

Yr = Ya + Y

Anomalous Behaviour of Water 

Most liquid except water expand when heated. This abnormal behavior of water is what is refer to as anomalous expansion of water. When water is heated from 00C, it contracts until it reaches 40C and beyond this point, water expands normally. The anomalous expansion of water takes place between 00C and 40C.

EVALUATION

1. With the aid of a diagram, explain the anomalous behavior of water.
2. Describe an experiment to determine the apparent cubic expansivity of a liquid

Reading Assignment

New School Physics pg 38 – 40,43 – 46

WEEKEND ASSIGNMENT

1. The anomalous expansion of water takes place between/at ………………..A. 10C and 40C B. 00C and 40C C. 40C and 250C D. all temperature
2. The SI unit of linear expansivity is ……… A. per Celsius B. per Fahrenheit C. per Kelvin D. per Joules
3. If the linear expansivity of a solid is 1.8 X 10 -6 k-1, the area expansivity will be

A.0.9 X 10 -6 B. 3.6 X 10 -6 C. 1.8 X 10 -6 D. 5.4 X 10-6

1. A metal of length 15.01m is heated until its temperature rises by 600C. If its new length is 15.05, calculate its linear expansivity

1. 0.0004/K B. 0.00004/K C. 0.004/K D. 0.04/K

1. The increase in volume of 10cm3 of mercury when the temperature rises by 1000C is 0.182cm3. What is the cubic expansivity of mercury A. 0.000182/K 

1. 0.0000182/K C. 0.000187/K D. 0.000178/K

THEORY

1. Explain the anomalous behavior of water
2. If a cube metal box made of iron of side 2cm is to be used for construction, and the expected temperature difference is 900C. What will be the expected change in volume of the cube box if the linear expansivity of iron is 1.25 X 10-5.