Linear Thermal Expansion Practice Problems

A suspension bridge is constructed using 8.0 m steel metal bars during winter when the temperature is 2.0°C. Determine the required spacing between the bars, such that they just come into contact (no compression) during the summer when the temperature is 42.0°C.

A hydraulic system has various parts like a barrel, rod, and piston. The piston fits tightly in the barrel and movements involve hydraulic oil and piston pushing on each other encased in the barrel.  Take the temperature of the hydraulic system to vary between 10°C and 180 °C, and that linear expansion coefficients are constant for the entire temperature range. If an aluminum piston fits in a copper barrel at 10°C, will the hydraulic work at the higher operating temperatures? Why?

A steel telecommunication tower constructed during the winter is measured to have a height of 502 ft when the temperature is 13.0°C. During the summer, the length of the tower is found to have increased by 0.138 ft. Determine the temperature during summer. It may be necessary to assume that the tower and the surroundings are in thermal equilibrium.

A 15.0 cm long metallic stick made of aluminum is placed in a temperature-controlled chamber at 15 °C. The stick is inserted between two fixed jaws, but it is found to be 35 μm shorter than required to fit perfectly. What temperature should the temperature-controlled chamber be so that the stick just fits between two fixed jaws?

A geologist studying stalagmite sediment rates in a 10 °C cave uses a 300.00 cm-long brass (accurate to 0.01 cm) measurement tool calibrated at 25 °C. The geologist quantifies stalagmite sediment to be 37.55 cm long. How should the geologist correct the values before publishing the results?

A steel bridge spanning a river experiences a temperature variation ΔT throughout a summer day. The bridge has a length of 75 meters at the coldest time of the day. Its length increases by 2.0 cm at the hottest time of the day. Calculate the temperature variation ΔT.

A ceramic tile walkway is constructed with individual tiles, each 16 m long, at a temperature of 18°C. The coefficient of thermal expansion of ceramic is α = 9.0 × 10⁻⁶/°C. If the temperature ranges from -20°C to +40°C, how wide should the expansion gaps between the tiles be (at 18°C) to prevent buckling?

To what temperature must you heat an aluminium rod to make it 1.8% longer than its length at 20°C? Assume the coefficient of linear expansion for aluminium is 2.30×10^-5 °C⁻¹.

A titanium bolt needs to be fitted into a copper sleeve. At 20 °C, the diameter of the bolt is 4.7 cm, while the inner diameter of the cylinder is 4.6 cm. At what common temperature should the bolt be exposed to in order to achieve a perfect fit in the sleeve?

[Hint: The thermal expansion coefficients of titanium and copper are 8.4 × 10^-6/ °C and 1.7 × 10^-5/ °C, respectively].

(A) Consider an iron rod of a cross-sectional area of 0.025 m² rigidly connected to two fixed horizontal supports. If the rod was installed at 15°C, what stress would develop if the temperature rose to 35°C? The iron rod’s thermal expansion coefficient is 12 x 10^-6 /°C, and Young's modulus is 200 GPa.

(B) Is the strength of the iron rod exceeded if it's known to be 370 MPa?

Suppose that a steel Tokyo Skytree which is 400 m tall, experiences a temperature change from 3.0 °C in January to 28 °C in July. Determine what the change in the height of the tower will be. Hint: Ignore the steel beam angles and treat the tower like a vertical beam.

A ring made of a nickel alloy is tightly fitted around a spherical object with a circumference of 1000 km at 20°C. If the temperature is increased to 50°C, how much will the ring rise from its initial position? Assume that it rises uniformly and the coefficient of linear expansion (α) for the nickel alloy is 1.2 × 10^-5 /°C. [Hint: β = 3α]

How much stress is required to keep an iron rod at its specified length if the temperature rises from 14 °C to 40 °C?

A meter scale made of copper can measure length correctly at a temperature of 20°C. If the temperature rises to 50°C, what will be the percentage error in its measurements due to thermal expansion? Assume that the coefficient of thermal expansion of copper is 1.7 × 10^-5/°C.

A clothesline made of steel is installed between two pillars separated by a distance of 40.0 m. In winter, at the temperature of -5.00 °C, the clothesline sags 4.50 cm. Make an approximation of the amount by which the clothesline sags in the summer at a temperature of 15.0 °C. Assume that the coefficient of thermal expansion of steel is 1.20 × 10^-5/°C. [Hint: The shape of the clothesline in the summer can be approximated by an arc of a circle. Also, equations that are not solvable analytically might be solved by trying out different values by trial and error.]

A solid metal cylinder with a diameter of 20.5 cm needs to be fitted with a circular brass frame. The frame has an inside diameter of 20.4 cm is at a temperature of 15.0°C, is 4.50 cm wide, and has a thickness of 0.520 cm. If the coefficient of linear expansion for brass is approximately 1.90 × 10^-5 /°C, (i) Calculate the minimum temperature that the frame must be heated to such that it can fit over the cylinder. (ii) After the frame has been fitted and it cools to 15.0°C again, what would be its tension? Assume that the Young's modulus for brass is 1.00 × 10¹¹ N/m².

A wooden block is floating in a container filled with water that is at a temperature of 15°C. If the temperature increases to 32°C, calculate the percentage value by which the fraction of the volume of the wood that is submerged in the water changes. Assume that, the coefficient of volume expansion of the wood is 4.5 × 10^-5/°C and water is 2.1 × 10^-4/°C respectively.

An aluminum cap fits snugly over an iron pipe at an initial temperature of - 5.0 °C. To loosen it, the assembly is warmed up to 45 °C. The internal diameter of the cap is 12.5 cm at - 5.0 °C. Calculate the new gap created between their radii after heating. Assume that the coefficient of linear expansion for aluminum and iron are 2.3 × 10^-5 /C° and 1.2 × 10^-5/C° respectively.

In case fluid gets filled up inside an elongated tubular vessel, such that it could expand primarily in one direction only, what is the relationship between effective linear expansion coefficient (α) and volumetric expansion coefficient (β).

For a tight fit, screws that are slightly larger than the screw hole are commonly used, with the screw being cooled before insertion into the hole. To what temperature must the screw be cooled for it to fit in the hole if a copper screw 1.875 cm in diameter is to be placed in a hole 1.873 cm in diameter in a metal plate at 25°C.[Coefficient of linear expansion of copper = 17 × 10^-6 /°C].

What force magnitude (F) should be applied to the ends of a 50-m-long copper rod of radius 5 mm to prevent it from elongation when its temperature increases by 25 °C?

The pendulum in a desk clock is made of aluminum and synchronized to give perfect time at 15°C. If the temperature changes, the clock loses its synchronization as its frequency depends on its length, just like a simple pendulum. Determine the time gained or lost in a month if the clock is kept at 25°C. [Hint: The coefficient of linear expansion for aluminum, α, is approximately 23 × 10^-6 °C^-1.]