Total translational kinetic energy

In summary, the conversation discusses the total translational kinetic energy of helium gas in a vessel at 0.0C and 1.00 atm. The equation for calculating this energy is 3/2KbT, where Kb is Boltzmann's constant and T is the temperature in Kelvins. However, the correct equation should include the number of molecules present in the vessel, N. By using the equation K = (3Nk_BT)/(2), the correct value of 4.5kJ can be obtained.
  • #1
[SOLVED] Total translational kinetic energy

1.A 0.03m3 vessel contains helium (monatomic) gas at 0.0C and 1.00 atm. The total translational kinetic energy of the gas molecules is (in KJ).

2. 3/2KbT


3. pV=nRT

where p is the pressure, V is the volume, n is the number of molecules present, R is the gas constant (8.31J/(mol*K)), and T is the temperature in Kelvins (273K = 0ºC)
The other equation is that the average translational kinetic energy K of a single molecule is

K = (3RT)/(2N)

where R and T are from the first equation and N is Avogadro's number (6.022E23).
Just sub in numbers:
K = (3 * 8.31 * 273) / ( 2 * 6.022E23) = 5.651E-21 Joules. This is the kinetic energy of one atom of helium at 0º C. Change the first equation around to get n = (pV) / (RT) and then multiply 5.65E-21 by n


The answer in the book shows its suppose to be 4.5kJ, but I'm yet to get that, I'm getting a way off number. Thanks for any help given :+)
 
Physics news on Phys.org
  • #2
2. 3/2KbT

This doesn't look right. It should be [tex] K = \frac{3Nk_BT}{2}[/tex] where N is the number of molecules in the vessel.

K = (3RT)/(2N)

Again, you are missing the N in the numerator. This equation is just the one above with a substitution for k_B.

If you have the N in the numerator, you will have a ratio of [tex]\frac{N}{N_A}[/tex] which is the number of moles of gas, n.

So just start over with the right equation and you should come out to the right answer.
 
  • #3
Awesome, Thanks for showing me where I made my mistake :+)
 

What is total translational kinetic energy?

Total translational kinetic energy is the sum of the kinetic energies of all the particles in a system that are moving in a straight line, also known as translational motion.

How is total translational kinetic energy calculated?

Total translational kinetic energy is calculated by multiplying the mass of an object by its velocity squared and dividing by 2. The formula for total kinetic energy is T = 1/2mv2.

What is the unit of measurement for total translational kinetic energy?

The unit of measurement for total translational kinetic energy is joules (J), which is the same unit used for all forms of energy.

What factors affect the total translational kinetic energy of a system?

The total translational kinetic energy of a system is affected by the mass and velocity of the particles within the system. A larger mass or higher velocity will result in a higher total kinetic energy.

How is the conservation of total translational kinetic energy applied in real-world situations?

The conservation of total translational kinetic energy is applied in real-world situations, such as collisions, where the total kinetic energy of a system remains constant before and after the collision. This principle is also used in the design of various machines and vehicles that rely on the transfer and conservation of kinetic energy.

Suggested for: Total translational kinetic energy

Back
Top