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By what ratio will the average velocity of the molecules in a gas change when the temperature is raised from 50°C to 200°C?
  • a)
    1.21/1
  • b)
    1.46/1
  • c)
    2/1
  • d)
    4/1
Correct answer is option 'A'. Can you explain this answer?
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By what ratio will the average velocity of the molecules in a gas chan...

This is the correct answer. If we take v200/v50, then we will get option b. But that is not according to the question.
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Explanation:

Given:
Initial temperature (T1) = 50°C
Final temperature (T2) = 200°C

Formula:
The average kinetic energy of gas molecules is directly proportional to the temperature of the gas in Kelvin.
Therefore, the average velocity of gas molecules is directly proportional to the square root of the temperature in Kelvin.

Conversion:
To convert Celsius to Kelvin, we use the formula: K = °C + 273.15
Initial temperature in Kelvin (T1) = 50 + 273.15 = 323.15 K
Final temperature in Kelvin (T2) = 200 + 273.15 = 473.15 K

Ratio Calculation:
Ratio of average velocities = √T2 / √T1
Ratio = √473.15 / √323.15 ≈ 1.21
Therefore, the ratio by which the average velocity of the molecules in a gas changes when the temperature is raised from 50°C to 200°C is approximately 1.21/1, which matches with option 'A'.
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