The kinetic energy per molecule is given by KE = 0.5 * m * v^2. Substituting v = 300 m/s gives the correct expression.

The RMS speed is proportional to the square root of the temperature. If the temperature is doubled, the RMS speed increases by a factor of sqrt(2). Therefore, the new RMS speed will be 300 * sqrt(2), which is approximately 600 m/s.

Using the formula v_rms = sqrt((3RT)/M), we can rearrange to find T: T = (M * v_rms^2) / (3R). Substituting M = 0.016 kg/mol and v_rms = 400 m/s gives T = 400 K.

The RMS speed increases with the square root of the temperature. Therefore, at 600 K, the RMS speed will be 400 * sqrt(2), which is approximately 800 m/s.

Kinetic energy per molecule = (1/2)mv^2. Using v = 400 m/s and m = M/N_A, we find KE = 0.5 mJ.

The average speed is related to RMS speed by the relation v_avg = (2/3) * v_rms. Thus, v_avg = (2/3) * 400 = 267 m/s.

The average speed of gas molecules is approximately 0.8 times the RMS speed, so average speed = 0.8 * 400 m/s = 320 m/s.

The speed at 1/2 of the RMS speed is simply 500 m/s / 2 = 250 m/s.

The average speed of gas molecules is related to the RMS speed by the relation v_avg = (v_rms * sqrt(8/3)). Therefore, the average speed is approximately 400 m/s.

The RMS speed is an average measure; individual molecular speeds will vary around this value.

Using v_rms = sqrt(3RT/M), we rearrange to find T = (v_rms^2 * M) / (3R). Plugging in values gives T approximately 300 K.

The RMS speed is proportional to the square root of the temperature. If the temperature is doubled, the RMS speed increases by a factor of sqrt(2).

The RMS speed is proportional to the square root of the temperature. If the temperature is doubled, the RMS speed increases by a factor of sqrt(2).

RMS speed is directly proportional to the square root of temperature. Halving the temperature results in a decrease in RMS speed by sqrt(2).

RMS speed increases by sqrt(4) = 2, since v_rms is proportional to sqrt(T).

RMS speed is proportional to the square root of temperature. Increasing from 300 K to 600 K increases the speed by sqrt(2).

The RMS speed of a mixture of gases is the weighted average of the RMS speeds of the individual components, taking into account their molar masses.

The RMS speed of a mixture of gases is calculated using the average molar mass of the mixture in the formula v_rms = sqrt((3RT)/M_avg).

The kinetic energy per molecule is given by KE = (1/2) * m * v^2. Thus, KE = 0.5 * m * (250)^2.

Speed of sound = sqrt(γRT/M) = sqrt(1.4 * (300^2)) = 400 m/s.

The speed of sound in a gas is given by c = sqrt(γRT/M). For an ideal gas, c is approximately 1.4 times the RMS speed.

The RMS speed is independent of the number of gas molecules; it depends only on temperature and molar mass.

At constant temperature, increasing pressure does not affect the RMS speed, as it is dependent on temperature and molar mass.

At constant volume, increasing pressure increases the temperature of the gas, which in turn increases the RMS speed.

Increasing the temperature increases the average kinetic energy of the molecules, resulting in a wider distribution of molecular speeds.

Increasing the temperature increases the RMS speed, as v_rms is proportional to the square root of temperature.

The kinetic energy of gas molecules is directly proportional to the square of the RMS speed, as KE = (1/2)mv_rms^2.

RMS speed is inversely proportional to the square root of molecular weight.

For an ideal gas, the RMS speed is always greater than the average speed due to the squaring of velocities in the RMS calculation.

For an ideal gas, the RMS speed is always greater than the average speed due to the nature of the distribution of molecular speeds.