A brass plug has a diameter of 10,000 cm at 20°C. To what temperature must it be cooled in order to fit into a hole A brass plug has a diameter of 10,000 cm at 20°C. To what temperature must it be cooled in order to fit into a hole with a diameter of 9,997 cm? (α =19× 10– 6)
By the definition of the linear thermal expansion we have:
here, is the increace in diameter of the brass plug when it is heated, is the initial diameter of the brass plug at some temperature , is the diameter of the brass plug at , is the linear expansion coefficient for steel, is the change in temperature.
From this formula we can find the change in temperature:
Finally, we can calculate the temperature at which the brass plug will fit exactly into a hole of constant diameter:
Answer:
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