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Thermal Expansion

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Hole Size A rectangular sheet of metal has a circular hole. What happens to the size of the hole when the metal is heated? A) It gets larger. B) It gets smaller. C) It stays the same.

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**Microscopic Spacing Atoms are in constant motion.**

Vibration increases with temperature Spacing increases with temperature

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Change in Volume The volume of matter expands when the atomic spacing increases. Increase temperature → increase volume. A volume increase is the same as a density decrease. T V T + DT V + DV

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**Coefficient of Volume Expansion**

For small volume changes the relationship between volume and temperature is linear. The coefficient of volume expansion is b. Material Coefficient b Quartz 1 x 10-6 C-1 Pyrex glass 9 x 10-6 C-1 Glass 27 x 10-6 C-1 Steel 35 x 10-6 C-1 Aluminum 75 x 10-6 C-1 Mercury 180 x 10-6 C-1 Water 210 x 10-6 C-1 Gasoline 950 x 10-6 C-1 Ethyl alcohol 1100 x 10-6 C-1 Air (1 atm) 3400 x 10-6 C-1

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Gas Tank A 72 L steel gas tank is open and filled to the top with gasoline, b = 950 x 10-6 C-1, at 18 C. The car sits in the sun and reaches a temperature of 32 C. How much gasoline overflows from the tank? The gasoline expands with temperature. Solve for DV = bV0 DT. (950 x 10-6 C-1)(72 L)(14 C) DV = 0.95 L The tank expansion was small in comparison. You get more gas if you fill it when it’s cool!

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**Cold Water Most substances expand uniformly with temperature.**

Water does not follow the pattern. Below 4 C water expands as it cools Very cold water stays on top Ice is even less dense

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**Stretching Solids Solids can have dimensions that are quite different.**

The long dimension may matter most. Focus on one dimension Other changes are still present, less magnitude T L T + DT L + DL

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**Linear Expansion The change in volume applies to the three dimensions.**

If the change is equal in all directions b is split in thirds. The coefficient of linear expansion in solids (a) is usually one third of b.

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Seasonal Changes The steel bed of a suspension bridge is 200 m long at 20 C. If the temperature goes from -30 C to +40 C, what contraction and expansion is possible? Use linear expansion. Solve for DL = aL0 DT. First in winter, (12 x 10-6 C-1)(200 m)(-50 C) DL = m Then in summer, (12 x 10-6 C-1)(200 m)(20 C) DL = m

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**Thermal Stress next A change in length is associated with a stress.**

Temperature change causes a change in length. If the stress is due to temperature, it’s a thermal stress. next

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