Calculating rms speed of hydrogen molecules

[amw2829]

Homework Statement

The rms speed of the molecules in 1.1 g of hydrogen gas is 1800 m/s.

500 J of work are done to compress the gas while, in the same process, 2000 J of heat energy are transferred from the gas to the environment. Afterward, what is the rms speed of the molecules?

I've already solved for the total translational energy(1800 J) before more work was done to the molecules. The thermal energy was also 3000 J.

Homework Equations

E = (5/3)(1/2)mv^2

The Attempt at a Solution

Since 500 J are compressed, and 2000 J are released, the energy would then be 300 J. I tried setting this equal to the above equation, but all answers I entered were wrong.

 

[ehild]

Homework Statement

The rms speed of the molecules in 1.1 g of hydrogen gas is 1800 m/s.

500 J of work are done to compress the gas while, in the same process, 2000 J of heat energy are transferred from the gas to the environment. Afterward, what is the rms speed of the molecules?

I've already solved for the total translational energy(1800 J) before more work was done to the molecules. The thermal energy was also 3000 J.

The Attempt at a Solution

Since 500 J are compressed, and 2000 J are released, the energy would then be 300 J. I tried setting this equal to the above equation, but all answers I entered were wrong.

300 J as final energy is wrong.
When compressing, work is done on the gas, increasing the internal energy. So 500 J is added, 2000 J heat removed.

ehild

 

[amw2829]

300 J as final energy is wrong.
When compressing, work is done on the gas, increasing the internal energy. So 500 J is added, 2000 J heat removed.

ehild

1800(Initial Energy) + 500 - 2000 = 300 J

Am I missing something or does the thermal energy also play a factor.

 

[ehild]

The work done and the heat removed changes the thermal energy, which is 5/2 RT for one mole of a diatomic molecule. ehild

 

[amw2829]

The work done and the heat removed changes the thermal energy, which is 5/2 RT for one mole of a diatomic molecule.


ehild

I took that approach and my answer was still wrong.

 

[ehild]

Could you show your work in detail?

ehild

 

[amw2829]

Could you show your work in detail?

ehild

3000 J(thermal energy_initial) + 500 J - 2000 = E thermal_final = 5/3(1/2)mv²

 

[ehild]

3000 J was the initial thermal energy . It decreased by 1500 J, the final thermal energy is 1500 J. The thermal energy is 5/3 (1/2 mv^2). So how much is 1/2 mv^2, the translational kinetic energy? How much is v, the rms speed? ehild