A frictionless piston of diameter D p = 50 mm, thickness = 10 mm, and density

A frictionless piston of diameter D_p = 50 mm, thickness δ = 10 mm, and density p = 8000 kg/m³ is placed in a vertical cylinder of total length L = 100 mm. The cylinder is bored into a material of very low thermal conductivity, and a mass of air M_a = 75 X 10^-6 kg is enclosed in the volume beneath the cylinder. The surroundings re at T_sur = 300 K while the bottom surface of the cylinder is maintained at T₁. The emissivity of all the surfaces is ε = 0.3.

What is the distance between the bottom of the piston and the bottom of the cylinder, L_b, for T₁ = 300, 450, and 600 K? What is the piston temperature?

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T = 300 K sur L = 100 mm Air Piston Tp Pp, & Lb 8 = 10 mm Heated surface T₁, 8 Dp = 50 mm