Lesson_1.5_Printable_PPT

# Lesson_1.5_Printable_PPT - Thermal Properties of Matter...

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Thermal Properties of Matter Thermal Expansion. Heat supplied to a material increases its internal energy, and causes the molecules to vibrate with larger amplitudes. As a result, each molecule now takes up a ttle more space than before and causes As a result of the expansion, its length, area and volume will change. little more space than before and causes the material to expand. We will consider each of these changes separately.

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(1) Change in Length When an object is heated, its increase in length L is proportional to its original length L o and the change in temperature T This can be written as: L = α L o T Here α is the constant of proportionality and is called the coefficient of linear expansion and is equal to the change in length per unit length per Kelvin change in temperature. It has the unit, per Kelvin ( K -1 ) o L L T α =
Experiment to measure α The arrangement shown above can be used to measure the length L 2 of the rod at a high temperature t 2 o C by passing steam through a jacket that contain the metal rod. The length of a metal rod L 1 is measured at the room temperature t 1 o C

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Experiment to measure α L = L 2 – L 1 T = t 2 – t 1 1 L L T α = 1 L L - 2 1 2 1 ( ) L t t = - L 2 – L 1 = α L 1 (t 2 – t 1 ) L 2 = L 1 + α L 1 (t 2 – t 1 ) L 2 = L 1 ( 1 + α T)
Similar expressions can be written for change in area with temperature as follows: (2) Change in area : A = β A T Here β is the constant of proportionality and is called the coefficient of area expansion. It is a measure of the increase in area per unit area per Kelvin rise in temperature .

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The coefficient of area expansion β can be calculated as: A 2 = A 1 [1 + β (t 2 – t 1 )] A A T β = 2 1 1 2 1 ( ) A A A t t - = - Since an area is made up of two lengths, an approximate relation between α and β can be written as: β = 2 α
Similar expressions can be written for change in volume with temperature as follows: Change in volume : V = γ V T ere the constant of proportionality and is Here γ is the constant of proportionality and is called the coefficient of volume expansion. It is a measure of the increase in volume per unit volume per Kelvin rise in temperature.

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The coefficient of volume expansion γ can be calculated as: V 2 = V 1 [1 + γ (t 2 – t 1 ) V V T γ = 2 1 1 2 1 ( ) V V V t t - = - Since volume is made up of three lengths, an approximate relation between α and γ can be written as: γ = 3 α
Approximate relations connecting α , β , and γ Assume that each of the following objects is heated by 1 K so that T = 1

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Values of α and γ of some common materials. Material α K -1 γ K -1 Aluminum 24 × 10 -6 75 × 10 -6 Brass 19 × 10 -6 56 × 10 -6 Copper 17 × 10 -6 50 × 10 -6 on or Steel 1 0 -6 5 0 -6 Iron or Steel 11 × 10 35 × 10 Lead 29 × 10 -6 87 × 10 -6 Ordinary glass 9 × 10 -6 18 × 10 -6 Gasoline 950 × 10 -6 Mercury 180 × 10 -6 Water 210 × 10 -6 Air 3400 × 10 -6
Change of density with temperature. When an object is heated, its mass remains

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## This note was uploaded on 05/01/2011 for the course PHY 2049 taught by Professor George during the Spring '11 term at Edison State College.

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Lesson_1.5_Printable_PPT - Thermal Properties of Matter...

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