The rms velocity of an oxygen molecule in a gas is 390 m/s. If the absolute temperature is increased by 20%, then what is the rms velocity?

The root mean square (rms) velocity of a gas is directly proportional to the square root of its absolute temperature. This relationship is expressed by the formula:

V2 = V1 * sqrt(T2/T1)

where:

• V1 is the initial rms velocity,
• V2 is the final rms velocity,
• T1 is the initial absolute temperature, and
• T2 is the final absolute temperature.

Given that the initial rms velocity (V1) is 390 m/s and the absolute temperature is increased by 20%, we can find the final rms velocity (V2) as follows:

1. First, we need to express the 20% increase in absolute temperature in terms of T1 and T2. If we let T1 represent the initial absolute temperature, then a 20% increase means that T2 = 1.20 * T1.

2. Next, we substitute these values into the formula:

V2 = 390 m/s * sqrt(1.20)

3. Finally, we calculate the square root of 1.20 and multiply it by 390 m/s to find V2.

Please note that without the initial temperature, we can't find the exact final velocity, but we can say that it will increase by a factor of sqrt(1.20) compared to the initial velocity.