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Thermal Expansion 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. Microscopic Spacing Atoms are in constant motion. • Vibration increases with temperature • Spacing increases with temperature 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 + T V + V V V0 T Coefficient of Volume Expansion For small volume changes the relationship between volume and temperature is linear. The coefficient of volume expansion is . V V0 T Material Quartz Pyrex glass Glass Steel Aluminum Mercury Water Gasoline Ethyl alcohol Air (1 atm) Coefficient 1 x 10-6 C-1 9 x 10-6 C-1 27 x 10-6 C-1 35 x 10-6 C-1 75 x 10-6 C-1 180 x 10-6 C-1 210 x 10-6 C-1 950 x 10-6 C-1 1100 x 10-6 C-1 3400 x 10-6 C-1 Gas Tank A 72 L steel gas tank is open and filled to the top with gasoline, = 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 V = V0 T. (950 x 10-6 C-1)(72 L)(14 C) V = 0.95 L The tank expansion was small in comparison. You get more gas if you fill it when it’s cool! 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 Stretching Solids Solids can have dimensions that are quite different. The long dimension may matter most. T L T + T L + L • Focus on one dimension • Other changes are still present, less magnitude Linear Expansion The change in volume applies to the three dimensions. If the change is equal in all directions is split in thirds. The coefficient of linear expansion in solids (a) is usually one third of . V0 L0 H 0W0 V LH 0W0 L0 HW0 L0 H 0 W V (T L0 (T 3 3 L0 H 0 (T H 0 )W0 L TaL0 a /3 L0 ) H 0W0 3 W0 ) 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 L = aL0 T. First in winter, (12 x 10-6 C-1)(200 m)(-50 C) L = -0.12 m Then in summer, (12 x 10-6 C-1)(200 m)(20 C) L = 0.048 m Thermal Stress A change in length is associated with a stress. F L Y A L0 Temperature change causes a change in length. L TaL0 If the stress is due to temperature, it’s a thermal stress. F TaYL0 aYT A L0 next