A steel ring with a hole having area of 7.970 cm2 is to be placed on an aluminum rod with cross-sectional area of 8.000 cm2. Both rod and ring are initially at a temperature of 29.0°C. At what common temperature can the steel ring be slipped onto one end of the aluminum rod? (The coefficient of linear expansion of steel is 11 ✕ 10−6 (°C)−1,  and the coefficient of linear expansion of aluminum is 24 ✕ 10−6 (°C)−1.)

A metal rod had a coefficient of linear expansion α = 1.5 x 10-5 1/K. It has a starting length of 210 cm. When the temperature changes from 25 °C to 55 °C, by how much does the length of the rod change, in cm?

A cramming student warms 0.500 L of cold coffee in a Pyrex carafe. Full carafe of coffee at 20°F. How much coffee has spilled when the coffee and carafe reach 95°C? Given that the carafe is an isotropic solid, Pyrex has a linear thermal expansion coefficient of 3.3 x 10-6 K-1 and water (coffee) has 207 x 106 K-1.

A pair of eyeglass frames are made of an epoxy plastic (coefficient of linear expansion = 1.30 10-4°C-1). At room temperature (20.0°C), the frames have circular lens holes 2.40 cm in radius. To what temperature must the frames be heated if lenses 2.41 cm in radius are to be inserted into them?

A cramming student warms 0.500 L of cold coffee in a Pyrex carafe. Full carafe of coffee at 20°F. How much coffee has spilled when the coffee and carafe reach 95°C? Given that the carafe is an isotropic solid, Pyrex has a linear thermal expansion coefficient of 3.3 x 10-6 K-1 and water (coffee) has 207 x 106 K-1.

A hollow aluminum cylinder 19.5 om deep has an internal capacity of 2.000 L at 21.0°C. It is completely filled with turpentine at 21.0°C. The turpentine and the aluminum cylinder are the slowly warmed together to 79.0°C. (The average linear expansion coefficient for aluminum is 24 x 10-c, and the average volume expansion coefficient for turpentine is 9.0 103) (a) How much turpentine overflows? cm³ (b) What is the volume of turpentine remaining in the cylinder at 79 0°C? (Give your answer to at least four significant figures) (c) If the combination with this amount of turpentine is then cooled back to 21.0°C, how far below the cylinder's rim does the turpentine's surface recede? om