The Physics
Hypertextbook
Opus in profectus

# Thermal Expansion

## Problems

### practice

1. Write something.
2. Write something else.
3. Write something different.
4. Write something completely different.

### numerical

1. A steel bridge is built in several segments, each 20 m long. The gap between segments is 4 cm at 18 °C. What is the maximum temperature that the bridge can manage before buckling?
2. Due to the high specific heat and low conductivity of water, only the uppermost 10% of the oceans is able to undergo any significant temperature change.
1. The natural variation in ocean levels is about 10 cm from September to March. By how much does the mean temperature of the upper ocean change during this time?
2. Global warming is likely to cause a rise in sea level for a number of reasons, one of which is the thermal expansion of water. Determine the rise in sea level for every 1.0 C° temperature increase in the upper ocean.
Data for the oceans
measurement value
surface area 3.61 × 1014 m2
mean depth 3794 m
mean temperature, overall 3.5 °C
mean temperature, top 10% 10 °C
3. How much taller is the Eiffel Tower on the hottest day of the summer than the coldest day of the winter? Assume the tower has a nominal height of 330 m measured from the top of the antenna. Also assume the entire tower is made of pure iron. (Actually, it's mostly made of "puddle iron". Extra credit if you can find a reliable expansivity for puddle iron.) Compute the change in height two different ways…
1. once using the extreme monthly average high and low temperatures
2. and again using the record high and low temperatures given in the table below
Paris, France: temperature statistics 1981–2010 and records (°C) Source: Meteo France
re­cord high date ave­rage high ave­rage ave­rage low re­cord low date
Jan­uary 16.1 05‑1999 7.2 4.9 2.7 −14.6 23‑1940
Feb­ruary 21.4 28‑1960 8.3 5.6 2.8 −14.7 02‑1956
March 26.0 31‑2021 12.2 8.8 5.3 −9.1 03‑1890
April 30.2 18‑1949 15.6 11.5 7.3 −3.5 13‑1879
May 34.8 29‑1944 19.6 15.2 10.9 −0.1 07‑1874
June 37.6 26‑1947 22.7 18.3 13.8 3.1 10‑1881
July 42.6 25‑2019 25.2 20.5 15.8 6.0 03‑1907
Aug­ust 39.5 11‑2003 25.0 20.3 15.7 6.3 29‑1881
Sep­tember 36.2 07‑1895 21.1 16.9 12.7 1.8 26‑1889
Oct­ober 28.9 01‑2011 16.3 13.0 9.6 −3.8 29‑1877
Nov­ember 21.6 07‑2015 10.8 8.3 5.8 −14.0 28‑1890
Dec­ember 17.1 16‑1989 7.5 5.5 3.4 −23.9 10‑1879
Year 42.6 2019 16.0 12.4 8.9 −23.9 1879
4. The Concorde was a supersonic transport airplane (SST) in use by British Airways and Air France from 1976–2003. At its cruising speed of 2170 km/h (2.04 times the speed of sound), friction with the air would heat the airframe to 120 °C. This caused the plane to stretch by about 20 cm. The dimensions of the Concorde are 61.66 × 25.6 × 8.5 m. Assume the temperature of the airframe when Concorde is on the ground is 20 °C.
1. Determine the coefficient of thermal expansion of the Concorde.
2. Use your results from part a. to determine the material used to construct the Concorde.
5. A 64 liter gas tank is filled completely at 15 °C. How much gasoline overflows, if the tank heats up to 35 °C while the car is parked in direct sunlight?
6. A 200 liter steel water tank is filled from a horizontal inlet pipe at the bottom. A vertical overflow pipe rises vertically from the top. Both pipes are 2.0 cm in diameter. How high does the water rise in the overflow pipe if the water is heated from 15 °C to 40 °C?
7. The underside of all US space shuttle orbiters were covered in lightweight, ceramic insulating tiles. These tiles varied in size and shape, but were basically 15 cm squares spaced 1.5 mm apart (at room temperature). They were designed to withstand reentry temperatures of up to +1260 °C. What is the approximate coefficient of thermal expansion of these tiles?

### statistical

1. Use the data from the following experiment to determine the volume expansivity of these eight liquefied gases. Source: M.J. Terry, et al. (1969).