Expansivity and Its Application - Linear, Area and Volume. Anomalous
SUBJECT: PHYSICS
CLASS: SS 1
DATE:
TERM: 2nd TERM
REFERENCE BOOK
WEEK FOUR
TOPIC: Expansivity and Its Application - Linear, Area and Volume. Anomalous
Expansion of Water. Real and Apparent Expansivity
CONTENT
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
â²L = L2 – L1
â²Ó¨ = Ó¨2 - Ó¨1 α = â²L
L1 â²Ó¨ ________ (ii)
α = L2 – L1
L1 X â²Ó¨
L2 – L1 = α L1 â²Ó¨
L2 = L1 + X L1 â²Ó¨
L2 = L1 (1 + X â²Ó¨)
N.B. â²L = L2 – L1
â²Ó¨ = Ó¨2 - Ó¨1
SOLUTION
L1 = 2m, L2 =?, â²Ó¨ = 100K, α = 18x1o-6k-1
L2 = L1 (1 + αâ²Ó¨)
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 â² Ó¨)
Similarly b2 = b1 (1 + α â² Ó¨)
A2 = L1 (1 + α â² Ó¨) X b1 (1 + α â² Ó¨)
= L1b1 (1 + α â² Ó¨) (1 + α â² Ó¨)
A2 = A1 (1 + 2 α â² Ó¨ + (α â²Ó¨) ²
A2 = A1 (1 + 2 α â² Ó¨)
A2 = A1 (1 + β â² Ó¨)
EVALUATION
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
Reading Assignment
New School Physics pg 38 – 40,43 – 46
WEEKEND ASSIGNMENT
A.0.9 X 10 -6 B. 3.6 X 10 -6 C. 1.8 X 10 -6 D. 5.4 X 10-6
THEORY
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