Concepts Of Physics MCQ Edition [Volume 2]PhysicsKinetic Theory of Gases
Suppose the molecules of a hydrogen sample possess a mean speed equal to the mean speed of the molecules of a helium sample. Determine the ratio of the temperature of the hydrogen sample to the temperature of the helium sample.
Options
- A2 : 1
- B1 : 2
- C1 : 2
- D2 : 1
Correct answer
C. 1 : 2
Step-by-step solution
The mean speed of gas molecules is given by v = 8RT M . Given that the mean speed of hydrogen molecules is equal to the mean speed of helium molecules: 8RT_ H₂ M_ H₂ = 8RT_ He M_ He Squaring both sides, we get: T_ H₂ M_ H₂ = T_ He M_ He T_ H₂ T_ He = M_ H₂ M_ He The molar mass of hydrogen gas ( H₂ ) is 2 g/mol and the molar mass of helium gas ( He ) is 4 g/mol. T_ H₂ T_ He = 2 4 = 1 2 The ratio of the temperature of the hydrogen sample to the temperature of the helium sample is 1 : 2 .