Week 4 – SS1 Second Term Physics Notes

 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 (Ө₂ – Ө₁) ______________ (i)
Linear expansivity (α)= increase in length                            
             Unit length x temp change
L₁ is the original length             Ө₁ is the initial temperature
L₂ is the final length                Ө₂ is the final temperature
▲L = L₂ – L₁
▲Ө = Ө₂ – Ө₁ 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

▲Ө = Ө₂ – Ө₁

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 (Ө₂ – Ө₁)
Recall; L₂ = L₁ (1 + α ▲ Ө)
Similarly b₂ = b₁ (1 + α ▲ Ө)
A₂ = L₁ (1 + α ▲ Ө) X b₁ (1 + α ▲ Ө)
= L₁b₁ (1 + α ▲ Ө) (1 + α ▲ Ө)
A₂ = A₁ (1 + 2 α ▲ Ө + (α ▲Ө) ²
A₂ = A₁ (1 + 2 α ▲ Ө)
A₂ = A₁ (1 + β ▲ Ө)

 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▲ Ө).

    
    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 (Ө₂ – Ө₁) ___________ (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
   

3. The anomalous expansion of water takes place between/at ………………..A. 1⁰C and 4⁰C B. 0⁰C and 4⁰C C. 4⁰C and 25⁰C D. all temperature
4. The SI unit of linear expansivity is ……… A. per Celsius B. per Fahrenheit C. per Kelvin D. per Joules
5. 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
   

6. 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

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

7. 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

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

    THEORY

8. Explain the anomalous behavior of water
9. 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.