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For a given gas at 1 atm pressure, rms speed of the molecules is 200 m/s at 127°C. At 2 atm pressure and at 227°C, the rms speed of the molecules will be:
- 100 m/s
- 80√5 m/s
- 100√5 m/s
- 80 m/s
Correct answer: 100√5 m/s
Solution
The root mean square (rms) speed of gas molecules is proportional to the square root of the temperature divided by the pressure. By applying the formula for rms speed and considering the changes in both temperature and pressure, we find that at 2 atm and 227°C, the rms speed calculates to 100√5 m/s.
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