Calculate RMS Speed of Helium at 361K

[R.Harmon]

"The composition of planetary atmospheres is determined in part by the speeds of the molecules of the constituent gases, because the faster moving molecules can reach escape velocity and leave the planet. Calculate the r.m.s. speed in meters per second of helium species at a temperature of 361 Kelvin."

Right, I have absolutely no idea where to start with this problem, so any formulas or guidance as to how to solve this would be greatly appreciated.

Thanks.

 

[stunner5000pt]

depeding on the course you're taking you should have done thermodynamics

$$v_{rms} = \sqrt{\frac{3RT}{M}}$$
where R is the universal gas constant, T is the temperature and M is the molar mass of the atoms involved.

 

[thepatientmental]

To calculate the RMS (root mean square) speed of helium at 361K, we can use the following formula:

RMS speed = √(3RT/M)

Where R is the gas constant (8.314 J/mol·K), T is the temperature in Kelvin, and M is the molar mass of helium (4.003 g/mol).

First, we need to convert the temperature from Kelvin to Celsius by subtracting 273.15. So, 361K is equal to 87.85°C.

Next, we need to convert the molar mass of helium from grams to kilograms. So, 4.003 g/mol is equal to 0.004003 kg/mol.

Now, we can plug in these values into the formula:

RMS speed = √(3 * 8.314 * 87.85 / 0.004003)

= √(2182.67)

= 46.7 m/s

Therefore, the RMS speed of helium at 361K is approximately 46.7 meters per second. This means that on average, the helium molecules in the atmosphere at this temperature are moving at a speed of 46.7 m/s. This information can be useful in understanding the composition and behavior of planetary atmospheres.