Thermodynamics: Internal Energy of a Gas

In summary, using the equations PV = nRT and U = 3/2nRT, it is determined that the internal energy of a 0.010-m^3 container filled with Helium gas at a pressure of 6.2 multiplied by 10^5 Pa is 9300J. To produce this amount of energy, a 0.38-hp engine would need to run for approximately 32.08 seconds. This calculation was made by relating power to energy and using the formula power = work / time.
  • #1
Azndoode1
11
0

Homework Statement


Helium (He), a monatomic gas, fills a 0.010-m^3 container. The pressure of the gas is 6.2 multiplied by 10^5 Pa. How long would a 0.38-hp engine have to run (1 hp = 746 W) to produce an amount of energy equal to the internal energy of this gas?



Homework Equations




Equations: DU = Q + W , Possibly PV = nRT?, Possibly DU = 3/2 n R T ?

The Attempt at a Solution


No idea how to go about doing this.
 
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  • #2
Use PV = nRT and U = 3/2nRTtherefore U=3/2(PV).R.
 
Last edited:
  • #3
So using that, I get U = 9300J,
P= 290.32 W,
So how do I find the time?
Thanks.
 
  • #4
Do you know how power and energy are related to each other?

Or, more simply, what is power?
 
  • #5
Power = work / time
I substituted in, got 23 seconds, and that is not the right answer...
am I doing something wrong?
 
  • #6
My power is 283.48W,
which gives t=32.8 s.
 
  • #7
I redid it and I got 32.08. I think I missed a decimal?
Thanks for the help... i'll try that.

EDIT: Yup it worked! Thanks very much :)
 

FAQ: Thermodynamics: Internal Energy of a Gas

What is the definition of internal energy in thermodynamics?

The internal energy of a gas is the total kinetic and potential energy of all the particles within the gas. It includes the random motion of the particles and their interactions with each other.

How is the internal energy of a gas related to its temperature?

The internal energy of a gas is directly proportional to its temperature. As the temperature increases, the average kinetic energy of the particles also increases, resulting in a higher internal energy.

What factors affect the internal energy of a gas?

The internal energy of a gas is affected by its temperature, pressure, and volume. Additionally, the type of gas, the number of particles, and any external work or heat added or removed can also impact the internal energy.

Can the internal energy of a gas change without any heat or work being added to it?

Yes, the internal energy of a gas can change due to the natural movement of particles within the gas. This is known as the internal energy of the gas changing due to its own internal forces, and is referred to as the internal energy of a gas being in a state of equilibrium.

How is the internal energy of a gas calculated?

The internal energy of a gas can be calculated using the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. It can also be calculated by multiplying the number of particles in the gas by the average kinetic energy of each particle.

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