Prof. Marlon Flores Sacedon Thermal Exansion Prof. Marlon Flores Sacedon Department of Mathematics and Physics College of Arts and Sciences Visayas State University, Visca Baybay City, Leyte, Phiippines

These are examples of Thermal Expansion Thermal expansion is the tendency of matter to change in shape, area, and volume in response to a change in temperature, through heat transfer. Most materials expand when their temperature increase. The decks of bridges need special joints and supports to allow for expansion. A completely filled and tightly capped bottle of water cracks when it is heated You can loosen a metal jar lid by running hot water over it. . These are examples of Thermal Expansion

Two Kinds of Thermal Expansion Linear Expansion Volume Expansion

Thermal Expansion

Thermal Expansion

Volume Expansion Linear Expansion T1 Lo T2 T2>T1 MFS

MFS Volume Expansion Linear Expansion T1 Lo L T2 @ T2 T2>T1 Vo @ T1 T1 Lo L T2 @ T2 T2>T1 T2>T1 Where: = coef. of linear expansion (1/K) L = change in length (m) L & Lo = final & initial length (m) T2&T1= final & initial temperature (oC) Where: = coef. of volume expansion (1/K) V = change in volume (m3) V & Vo = final & initial volume (m3) T2&T1= final & initial temperature (oC) MFS

MFS Coefficients of Linear Expansion Coefficients of Volume Expansion Material [K-1 or (Co)-1] Aluminum 2.4x10-5 Brass 2.0x10-5 Copper 1.7x10-5 Glass 0.4-0.9x10-5 Invar 0.09x10-5 Quartz 0.04x10-5 Steel 1.2x10-5 Material [K-1 or (Co)-1] Aluminum 7.2x10-5 Brass 6.0x10-5 Copper 5.110-5 Glass 1.2-2.7x10-5 Invar 0.27x10-5 Quartz 0.12x10-5 Steel 3.6x10-5 Ethanol 75x10-5 Carbon Disulfide 115x10-5 Glycerine 49x10-5 Mercury 18x10-5 MFS

Relationship between coefficient of volume expansion & coefficient of linear expansion Recall:

MFS Coefficients of Linear Expansion Coefficients of Volume Expansion Material [K-1 or (Co)-1] Aluminum 2.4x10-5 Brass 2.0x10-5 Copper 1.7x10-5 Glass 0.4-0.9x10-5 Invar 0.09x10-5 Quartz 0.04x10-5 Steel 1.2x10-5 Material [K-1 or (Co)-1] Aluminum 7.2x10-5 Brass 6.0x10-5 Copper 5.110-5 Glass 1.2-2.7x10-5 Invar 0.27x10-5 Quartz 0.12x10-5 Steel 3.6x10-5 Ethanol 75x10-5 Carbon Disulfide 115x10-5 Glycerine 49x10-5 Mercury 18x10-5 Relationship between coefficient of volume expansion & coefficient of linear expansion MFS

Example 1: A surveyor uses a steel measuring tape that is exactly 50 Example 1: A surveyor uses a steel measuring tape that is exactly 50.000 m long at a temperature of 20 oC. What is its length on a hot summer day when the temperature is 35 oC? Lo Solution 50 m Temperature of tape @ 20oC L = ? Temperature of tape @ 35oC From table, the coefficient of linear expansion From the formula: MFS Ans Transforming = 50.009 m

Example 3: A glass flask with volume 200 cm3 is filled to the brim with mercury at 20 oC. How much mercury overflows when the temperature of the system is raised to 100 oC? The coefficient of linear expansion of the glass is 0.40x10-5 K-1. Solution Mercury overflows ( Vover) Mercury, expanded volume( VHg) Glass flask, expanded volume ( Vglass) Mercury column Glass flask From table: Glass flask filled w/ mercury @ T1=20oC @ T2=100oC Answer: ∆ 𝑽 𝒐𝒗𝒆𝒓 =𝟐.𝟕 𝒄𝒎 𝟑

Seat Work1: The Humber Bridge in England has the world’s longest single span, 1410m in length. Calculate the change in length of steel deck of the span when the temperature increases from -5.0oC to 18.0oC. Answer: 0.39 m Seat Work2: A metal rod is 40.125 cm long at 20.0oC and 40.148 cm long at 45.0oC. Calculate the average coefficient of linear expansion of the rod for this temperature range. Answer: 2.3x10-5 (Co)-1 Seat Work3: A glass flask whose volume is 1000.00 cm3 at 0.0oC is completely filled with mercury at this temperature. When flask and mercury are warmed to 55.0oC, 8.95 cm3 of mercury overflow. If the coefficient of volume expansion of mercury is 18.0x10-5 K-1, compute the coefficient of volume expansion of the glass. Answer: 1.7x10-5 (Co)-1

Assignment 1) A Pendulum shaft of a clock is made of brass. What is the fractional change in length of the shaft when it is cooled from 19.50oC to 5.00oC? Answer: -2.9x10-4 2) An underground tank with a capacity of 1700L (1.70m3) is filled with ethanol that has an initial temperature of 19.0oC. After the ethanol has cooled off to the temperature of the tank and ground, which is 10.0oC, how much air space will there be above the ethanol in the tank? (Assume that the volume of the tank doesn’t change.) Answer: 2.3x10-5 (Co)-1 3) A metal rod that is 30.0 cm long expands by 0.0650 cm when its temperature is raised from 0oC to 100oC. A rod of a different metal and of the same length expands by 0.0350 cm for the same rise in temperature. A third rod, also 30.0 cm long is made up of pieces of each of the above metals placed end-to-end and expands 0.0580 cm between 0oC and 100oC. Find the length of each portion of the composite bar. Answer: 23.0cm, 7.0cm

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