Thermal Expansion

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

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

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!

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. Focus on one dimension Other changes are still present, less magnitude T L T + DT L + DL

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.

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 = -0.12 m Then in summer, (12 x 10-6 C-1)(200 m)(20 C) DL = 0.048 m

Thermal Stress 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.