1. A metal ring with the inner radius of r1 and the outer radius of r2,and a metal disk of radius R with a sector of angle ? missing are heated uniformly so that their temperatures change by ?T. Both the ring and the disk are made of the same metal with the coefficient of linear expansion α. Determine the change in the inner and the outer radii of the ring and the angle of the sector in the disk. Find the change in the areas of the ring and the disk. Calculate these changes for the case when α = 17 · 10-6 K-1, ?T = 10 K,r1 = 10 cm, r2 = 20 cm, R = 20 cm. In your solution, neglect any terms quadratic in α.
2. The energy flux 1 coming from the night sky is 2·10-6 W/m2. Using this quantity, estimate the temperature of the intergalactic dust. The Stefan-Boltzmann constant is 5.
67 · 10-8 W/ m2 · K4.