You and your team are testing a device that is to be submerged in the cold waters of Antarctica. It is designed to rotate a small wheel at a very precise rate. One component of the device consists of a steel wheel (diameter D_steel = 3.0000 cm at T = 78.400 °F) and a large aluminum wheel that drives it (diameter D_Al = 150.000 cm at T = 78.400 °F).

(a) If the aluminum wheel rotates at 35.0000 RPM, at what rate does the smaller, steel wheel turn while both wheels are at T = 78.400 °F?

(b) You submerge the device in a large vat of water held at 32.800 °C, simulating its working environment in the Antarctic seas. Assuming the larger, aluminum driving wheel still rotates at 35.0000 RPM, at what rate does the smaller, steel wheel rotate when the device is submerged in the cold water?

(c) How should you adjust the rate of the aluminum driving wheel so that the steel wheel rotates at the same rate as it had at T = 78.400 °F? α_Al = 23 × 10⁻⁶ and α_steel = 12 × 10⁻⁶.