2 Hole 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.
3 Microscopic Spacing Atoms are in constant motion. Vibration increases with temperatureSpacing increases with temperature
4 Change 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
5 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 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
6 Gas 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!
7 Cold 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
8 Stretching 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
9 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.
10 Seasonal 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
11 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