1. What would be the final temperature of a mixture of 50 g of 20°C water and 50 g of 40°C water?
2. Suppose that a brass rod 1.0 m long expands 0.5 cm when its temperature is increased a certain amount. By how much will a brass rod 100 m long expand with the same change of temperature?
3. Steel expands 11 parts in a million for each 1°C change. Think about the 1.3-km main span of steel for the Golden Gate Bridge. If the span had no expansion joints, show that the span would be 0.21 m longer for a 15°C increase in temperature. [Use the formula ΔL = αLoΔT, where Lo is the original length, α is the "coefficient of expansion" that for steel is (1/1,000,000) per °C, and ΔT is the change in temperature.]
4. Consider a 40,000-km steel pipe that forms a ring to fit snugly all around the circumference of the Earth. Suppose people along its length breathe on it so as to raise its temperature 1°C. The pipe gets longer. It also is no longer snug. How high does it stand above ground level? (To simplify, consider only the expansion of its radial distance from the center of Earth, and apply the geometry formula that relates circumference C and radius r, C = 2πr. The result is surprising!)