Question

Cylinder A contains a gas whose molecules have an average speed of 0.0000001 meters/sec. Cylinder B contains a gas whose molecules have an average speed of 0.3 meters/sec. Select the statement below that is true regarding these cylinders. options: Cylinder A contains a gas that has a temperature closest to absolute zero. Even though the molecules are moving at different speeds in the two cylinders, they have the same kinetic energy. Cylinder B contains molecules that are moving more slowly than the molecules in Cylinder A. Cylinder B contains a gas that has a temperature closest to absolute zero.

Answer 1

The correct option is;

Cylinder A contains a gas that has a temperature closest to absolute zero

Step-by-step explanation:

From the kinetic theory of gases, the average speed of a gaseous molecule is found from the following equation;

`v_(rms) = \sqrt{(3\cdot R \cdot T)/(MW) }`

Where:

`v_(rms)` = rms speed which is the square root of the average of the velocities of the gas molecules squared which is used in place of the average of the gas molecules as the sum of the velocities of all the gas molecules in the cylinder is zero

R = Universal gas constant = 8.3145 J/(mol·K)

MW = Molecular weight of the gas

Hence where we have;

`v_(rmsA)` = Average velocity of gas A = 0.0000001 m/s

`v_(rmsB)` = Average velocity of gas B = 0.3 m/s

Since, R and MW are constant for the gas in cylinder A constant, therefore, as
`v_(rmsA)` ≈ 0 m/s, the temperature,
`T_A`, of gas A is closest to absolute zero.