Stefan-Boltzmann law. Thermal radiation by a grey body.

**33. ssm A solid cylinder is radiating power. It has a length that is ten times its radius. It is cut into a number of smaller cylinders, each of which has the same length. Each small cylinder has the same temperature as the original cylinder. The total radiant power emitted by the pieces is twice that emitted by the original cylinder. How many smaller cylinders are there?

A small sphere (emissivity = 0.745, radius = r1) is located at the center of a spherical asbestos shell (thickness = 1.72 cm, outer radius = r2; thermal conductivity of asbestos is 0.090 J/(s m Co)). The thickness of the shell is small compared to the inner and outer radii of the shell. The temperature of the small sphere is 727 °C, while the temperature of the inner surface of the shell is 406 °C, both temperatures remaining constant. Assuming that r2/r1 = 6.54 and ignoring any air inside the shell, find the temperature in degrees Celsius of the outer surface of the shell.

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