Example 1A concrete sidewalk is constructed between two buildings on a day when the temperature is 25ºC. The sidewalk consists of two slabs, each 3m in length and of negligible thickness. As the temperature rises to 38ºC, the slabs expand, but no space is provided for thermal expansion. The buildings do not move, so the slabs buckle upward. Determine the vertical distance y in the drawing.

Example 2The aluminum lid of a jar of dill pickles is stuck to the jar. To loosen the lid so it can be opened, hot water is poured over the lid causing it to expand. If the temp. increase of the lid and the glass is 40C°, calculate the change in circumference of the lid and the glass on which it is screwed. The diameter of the lid before heating is 22cm.

Example 3A metal rod (metal A) that is 30 cm long expands by 0.0750 cm when its temperature is raised from 0.0ºC to 100ºC. A rod of a different material (metal B) and of the same length expands by 0.040 cm for the same rise in temperature. A third rod, also 30 cm long , is made up of pieces of each of the above metals placed end to end and expands 0.0550 cm between 0ºC and 100 ºC Find each portion of the composite bars.

Example 1A steel tank is completely filled with 2.80 m3 of ethanol. Both the tank and ethanol at a temperature of 32.2°C. When the tank and its contents have cooled to 18ºC, what additional volume of ethanol can be put into the tank?

= 75 x / = 3.6 x /

Example 2A glass flask whose volume is 1000 cm3 at 0.0ºC is completely filled with mercury at this temperature. When the flask and mercury are warmed to 55.0ºC, 8.95 cm3 of mercury overflows. Compute the coefficient of volume expansion of the glass.

= 18 x /

Seatwork

Thermal Stress

• Develops when one tries to prevent the contraction or expansion of a material being subjected to temperature change

• The reason why bridges usually have gaps between sections is to permit expansion or contraction to occur without thermal stresses developing.

• Tensile stress happens when a rod with length Lo and cross section area A is held at constant length while the temperature is reduced (negative ∆T)[ or increased (positive ∆T) ]

• The fractional change in length of the rod was free to contract would be

=

where both and are negative (or positive).

Thermal Stress

• The tension must increase by an amount F that is just enough to produce an equal and opposite fractional change in length given by

= stress = strain

where is the Young’s Modulus of the rod.

• Keeping the length constant, the total fractional change in length must be zero. Therefore, the tensile stress needed to keep the rod’s length constant is

Thermal Stress

Thermal Stress