Thermodynamics- rms translational kinetic energy

[yaykey428]

Homework Statement

A container having a volume of 1m^3 holds 5 moles of helium gas at 50C. If the helium behaves like an ideal gas, the rms translational kinetic energy is?

Homework Equations

Total E= 3/2 nRT

The Attempt at a Solution

I tried solving this question using this equation, but I did not get the right answer.
The correct answer is 6.7 x 10^-21 J

 

[ehild]

Welcome to PF!

Please, show your work. ehild

 

[yaykey428]

Total Ek= 3/2 nRT
= 3/2 x 5 x 8.314 x 323
= 20140.7J, but this answer is wrong

 

[vela]

The problem is asking for the energy per atom.

 

[Nickie]

.

As a scientist, it is important to understand that the equation provided (Total E= 3/2 nRT) is only applicable for an ideal gas under certain conditions. In order to accurately calculate the rms translational kinetic energy, we need to use the equation E = (3/2)kT, where k is the Boltzmann constant and T is the temperature in Kelvin.

In this case, we have the volume, number of moles, and temperature of the helium gas. We can use the ideal gas law (PV = nRT) to calculate the pressure of the gas, which is necessary for our calculation. Once we have the pressure, we can then use the equation E = (3/2)kT to calculate the rms translational kinetic energy, which is equal to the average kinetic energy of the gas molecules.

Using this method, we get a value of 6.7 x 10^-21 J, which is the correct answer. It is important to note that the rms translational kinetic energy is a measure of the average kinetic energy of the gas molecules, and it is directly proportional to the temperature of the gas. Therefore, the higher the temperature, the higher the rms translational kinetic energy.