Thermal Expansion and its Effects

Temperature and Heat (Continuation…)

Questions About Thermal Expansion

Question 1: Aluminum and Steel Parts
  • Scenario: Aluminum parts held together by steel screws are stuck.
  • Question: What action should be taken to disassemble them?
  • Options:
    • A. Heat the assembly up.
    • B. Cool the assembly down.
    • C. Blow the assembly up.
Question 2: Steel and Aluminum Parts (Reversed)
  • Scenario: Steel parts held together by aluminum screws are stuck.
  • Question: What action should be taken to disassemble them?
  • Options:
    • A. Heat the assembly up.
    • B. Cool the assembly down.
    • C. Blow the assembly up.
Question 3: Mercury-in-Glass Thermometer
  • Observation: When a mercury-in-glass thermometer is inserted into a hot liquid, the mercury column initially drops before rising.
  • Question: How can this initial drop be explained?
  • Options:
    • A. The mercury contracts before the glass contracts.
    • B. The glass contracts before the mercury contracts.
    • C. The mercury contracts while the glass expands.
    • D. The glass starts to expand before the mercury expands, but mercury expands faster after that.
    • E. The mercury starts to expand before the glass expands, then mercury continues to expand faster.
Question 4: Mercury and Glass with Same Expansion Coefficient
  • Hypothetical: Suppose liquid mercury and glass had the same coefficient of volume expansion.
  • Question: Would a mercury-in-glass thermometer still function?
  • Options:
    • A. Yes
    • B. No
    • C. Cannot say
Question 5: Stuck Drinking Glasses
  • Scenario: Two drinking glasses are stuck together, one inside the other.
  • Question: How can they be unstuck?
  • Options:
    • A. Run hot water over both glasses.
    • B. Put hot water in the inner glass.
    • C. Run hot water over the outer glass.
    • D. Run cold water over both glasses.
    • E. Break the glasses.
Question 6: Steel Tape Measure on a Hot Day
  • Scenario: A steel tape measure gives accurate length measurements at room temperature but is used outside on a very hot day.
  • Question: How will the high temperature affect its length measurements?
  • Options:
    • A. Measured lengths will be too small.
    • B. Measured lengths will still be accurate.
    • C. Measured lengths will be too big.
Question 7: Expansion of a Hole in a Brass Plate
  • Scenario: A thin brass plate with a circular hole is heated.
  • Question: What will happen to the size of the hole?
  • Options:
    • A. The hole gets larger.
    • B. The hole gets smaller.
    • C. The hole stays the same.
    • D. The hole vanishes.

Linear Thermal Expansion Examples

The Expansion of Holes
  • Material expands when heated.
  • A hole in a solid material expands when heated and contracts when cooled, behaving as if it were filled with the surrounding material.
Question 8: Rod and Aluminum Frame (Aluminum Rod)
  • Scenario: A rod is hung from an aluminum frame with a small gap between the rod and the floor. The frame and rod are initially at the same temperature and then heated uniformly. The rod is made of Aluminum.
  • Question: Will the rod ever touch the floor?
  • Options:
    • A. Yes
    • B. No
  • Coefficients of linear thermal expansion ($\alpha$ in ℃$^{-1}$):
    • Aluminum: 23×10−623 \times 10^{-6}
    • Lead: 29×10−629 \times 10^{-6}
    • Brass: 19×10−619 \times 10^{-6}
Question 9: Rod and Aluminum Frame (Lead Rod)
  • Scenario: Same setup as above, but now the rod is made of Lead.
  • Question: Will the rod ever touch the floor?
  • Options:
    • A. Yes
    • B. No
  • Coefficients of linear thermal expansion ($\alpha$ in ℃$^{-1}$):
    • Aluminum: 23×10−623 \times 10^{-6}
    • Lead: 29×10−629 \times 10^{-6}
    • Brass: 19×10−619 \times 10^{-6}
Question 10: Rod and Aluminum Frame (Brass Rod)
  • Scenario: Same setup as above, but now the rod is made of Brass.
  • Question: Will the rod ever touch the floor?
  • Options:
    • A. Yes
    • B. No
  • Coefficients of linear thermal expansion ($\alpha$ in ℃$^{-1}$):
    • Aluminum: 23×10−623 \times 10^{-6}
    • Lead: 29×10−629 \times 10^{-6}
    • Brass: 19×10−619 \times 10^{-6}

Buckling of a Sidewalk

Scenario
  • A concrete sidewalk is constructed between two buildings at 25℃.
  • The sidewalk consists of two slabs, each three meters in length with negligible thickness.
  • Assume linear expansion along the length only.
Buckling Phenomenon
  • As temperature rises, the slabs expand, but there is no space for thermal expansion.
  • The buildings do not move, so the slabs buckle upward.
Calculating Vertical Distance
  • Use the linear thermal expansion formula to find the length of the expanded slab: ΔL=L−L<em>0=αL</em>0ΔT\Delta L = L - L<em>0 = \alpha L</em>0 \Delta T
  • L=αL<em>0ΔT+L</em>0L = \alpha L<em>0 \Delta T + L</em>0
  • Use trigonometry to find the height (y) by which the slabs push each other and rise.
Implications
  • Buckling is a consequence of not providing sufficient room for thermal expansion.
  • Engineers incorporate expansion joints or spaces at intervals along bridge roadbeds to prevent such problems.