The first real length standard, adopted more than 200 years ago, was a platinum bar with two very fine marks separated by what was defined to be exactly one meter. If this standard bar was to be accurate to within +1.0 µm, how carefully would the trustees have needed to control the temperature? The coefficient of linear expansion is 9 × 10-6/C°.

A spherical steel ball bearing has a diameter of 2.540 cm at 26.00°C. (Assume the coefficient of linear expansion of the steel is 1.10 10-5(°C-1), and the average volume expansion coefficient is 3.30 10-5(°C-1).) A) What is its diameter when its temperature is raised to 97.0°C? (Give your answer to four significant figures in cm.) B) What temperature change is required to increase its volume by 1.100%?

a) What is the percentage increase in temperature between 0°C and 26°C when the temperatures are measured in Kelvin? What is the difference between these two temperatures when measured in Kelvin? The outlet of a rocket engine has a cylindrical shape. Its diameter is 2.5m when constructed in the factory at 18°C. Given a = 6 x 10-6K-1 for the alloy used, what will its diameter be (in metres) at its operating temperature of 600°C ? d) What will the cross-sectional area of the outlet be (in m²) at this temperature?