2Hole SizeA 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.
3Microscopic Spacing Atoms are in constant motion. Vibration increases with temperatureSpacing increases with temperature
4Change in VolumeThe volume of matter expands when the atomic spacing increases.Increase temperature → increase volume.A volume increase is the same as a density decrease.TVT + DTV + DV
5Coefficient of Volume Expansion For small volume changes the relationship between volume and temperature is linear.The coefficient of volume expansion is b.Material Coefficient bQuartz 1 x 10-6 C-1Pyrex glass 9 x 10-6 C-1Glass 27 x 10-6 C-1Steel 35 x 10-6 C-1Aluminum 75 x 10-6 C-1Mercury 180 x 10-6 C-1Water 210 x 10-6 C-1Gasoline 950 x 10-6 C-1Ethyl alcohol 1100 x 10-6 C-1Air (1 atm) 3400 x 10-6 C-1
6Gas TankA 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 LThe tank expansion was small in comparison.You get more gas if you fill it when it’s cool!
7Cold Water Most substances expand uniformly with temperature. Water does not follow the pattern.Below 4 C water expands as it coolsVery cold water stays on topIce is even less dense
8Stretching Solids Solids can have dimensions that are quite different. The long dimension may matter most.Focus on one dimensionOther changes are still present, less magnitudeTLT + DTL + DL
9Linear 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.
10Seasonal ChangesThe 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 = mThen in summer,(12 x 10-6 C-1)(200 m)(20 C)DL = m
11Thermal 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