Draw a neat labelled diagram of Ferry's perfectly black body.Compare the rms speed of hydrogen molecules at 227ºC with rms speed of oxygen molecule at 127ºC. Given that molecular masses of hydrogen and oxygen are 2 and 32 respectively.

Answer: Diagram as described below; \(\dfrac{v_{H}}{v_{O}} = \sqrt{20} \approx 4.47\), i.e. \(v_H : v_O \approx 4.47 : 1\).

Ferry's perfectly black body: [Diagram: a double-walled hollow metal sphere; space between the walls evacuated; inner surface coated with lamp black; a small hole (aperture) on one side; a conical projection on the inner wall exactly opposite the hole; label radiation entering through the hole and undergoing multiple reflections.]

• It is a double-walled hollow sphere with a tiny hole; the space between the walls is evacuated to prevent heat loss by conduction and convection.
• The inner surface is coated with lamp black; a conical projection opposite the hole prevents direct reflection of the incident ray back out of the hole.
• Radiation entering the hole suffers multiple reflections inside and is completely absorbed, so the hole acts as a perfectly black body. When heated, radiation coming out of the hole is black-body radiation.

Numerical: \(T_H = 227 + 273 = 500\) K, \(T_O = 127 + 273 = 400\) K, \(M_H = 2\), \(M_O = 32\).

\(v_{rms} = \sqrt{\dfrac{3RT}{M}}\), so \(\dfrac{v_H}{v_O} = \sqrt{\dfrac{T_H}{T_O}\times\dfrac{M_O}{M_H}} = \sqrt{\dfrac{500}{400}\times\dfrac{32}{2}} = \sqrt{1.25\times16} = \sqrt{20}\)

\(\dfrac{v_H}{v_O} = 4.472\). The rms speed of hydrogen at 227 °C is about 4.47 times that of oxygen at 127 °C.