Question

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

Hint:

The rms speed of gas molecules is inversely proportional to the square root of their molecular mass. Hence, lighter molecules (such as hydrogen) move faster than heavier ones (like oxygen) at the same temperature.

Answer 1

Ferry's perfectly black body diagram shows an idealized body that absorbs all incident radiation and reflects none. It is used in experiments to study the emission of radiation at different temperatures. The diagram for Ferry's perfectly black body consists of a cavity with a small hole on one side that allows radiation to enter. The body absorbs all radiation that enters, making it a perfect absorber. 

rms speed comparison:
The root mean square (rms) speed \( v_{{rms}} \) of a gas molecule is given by the equation: \[ v_{{rms}} = \sqrt{\frac{3kT}{m}} \] where: - \( k \) is the Boltzmann constant, 
- \( T \) is the temperature in Kelvin, 
- \( m \) is the mass of a molecule. For hydrogen at \( 227^\circ {C} \) (\( T_1 = 227 + 273 = 500 \, {K} \)) and oxygen at \( 127^\circ {C} \) (\( T_2 = 127 + 273 = 400 \, {K} \)):

\[ v_{{rms, H_2}} = \sqrt{\frac{3k(500)}{2}} \quad \text{and} \quad v_{{rms, O_2}} = \sqrt{\frac{3k(400)}{32}} \]

Taking the ratio of the rms speeds:

\[ \frac{v_{{rms, H_2}}}{v_{{rms, O_2}}} = \sqrt{\frac{500 \times 32}{400 \times 2}} = \sqrt{\frac{16000}{800}} = \sqrt{20} \approx 4.472 \]

Thus, the rms speed of hydrogen molecules is approximately \( 4.472 \) times the rms speed of oxygen molecules.