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Difficulty: MediumPostulates of Kinetic Theory and States of Matter

A closed vessel contains a sample of oxygen gas at an initial temperature of 127∘C127^\circ\text{C}. According to the kinetic theory of gases, if heat is added until the average kinetic energy of the gas molecules is exactly doubled, what is the final temperature of the gas in degrees Celsius?

  1. 527∘C527^\circ\text{C}Answer
  2. B
    254∘C254^\circ\text{C}
  3. C
    800∘C800^\circ\text{C}
  4. D
    1073∘C1073^\circ\text{C}

Answer

The final temperature of the gas is 527∘C527^\circ\text{C}.
According to the kinetic molecular theory, the average kinetic energy of gas particles is directly proportional to the absolute temperature in Kelvin (Ek∝TE_k \propto T). Converting the initial temperature to Kelvin gives 127+273=400 K127 + 273 = 400\text{ K}. Doubling the average kinetic energy doubles the absolute temperature to 800 K800\text{ K}. Converting 800 K800\text{ K} back to degrees Celsius yields 800−273=527∘C800 - 273 = 527^\circ\text{C}.

Step-by-Step Solution

1
Convert the initial temperature from degrees Celsius to Kelvin
T1=127∘C+273=400 KT_1 = 127^\circ\text{C} + 273 = 400\text{ K}
According to the kinetic theory of gases, average kinetic energy is directly proportional to absolute temperature in Kelvin (Ek∝TE_k \propto T).
2
Calculate the final absolute temperature after doubling the average kinetic energy
T2=2×400 K=800 KT_2 = 2 \times 400\text{ K} = 800\text{ K}
Since average kinetic energy is doubled, the absolute temperature must also double.
3
Convert the final temperature back to degrees Celsius
T2,∘C=800 K−273=527∘CT_{2,^\circ\text{C}} = 800\text{ K} - 273 = 527^\circ\text{C}
The question asks for the final temperature in degrees Celsius.

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Postulates of Kinetic Theory and States of Matter
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Postulates of Kinetic Theory and States of Matter