The average kinetic energy of gas molecules is proportional to the absolute temperature. The table shows the average kinetic energy at four temperatures. Te...
Question 1 Report
The average kinetic energy of gas molecules is proportional to the absolute temperature. The table shows the average kinetic energy at four temperatures.
| Temperature / K | Average kinetic energy / 10−21 J |
|---|---|
| 200 | 4.2 |
| 400 | 8.4 |
| 600 | 12.6 |
| 800 | X |
What is the value of X?
Answer Details
The average kinetic energy of gas molecules is directly proportional to the absolute temperature in kelvin. This means that doubling the temperature doubles the average kinetic energy.
From the data, at 200 K the average kinetic energy is 4.2 × 10−21 J. The constant of proportionality is 4.2 / 200 = 0.021 × 10−21 J K−1. At 800 K, the kinetic energy is 0.021 × 800 = 16.8 (in units of 10−21 J). This can also be seen from the pattern in the table: each 200 K increase adds 4.2, so at 800 K the value is 12.6 + 4.2 = 16.8.
Any answer that does not maintain this linear proportionality breaks the fundamental relationship between temperature and kinetic energy. A quick check is that 800 K is four times 200 K, and 16.8 is indeed four times 4.2.
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