Internal Energy of an ideal gas

In summary, the question deals with the change in internal energy of an ideal gas with a constant temperature and initial pressure. The correct formula to use is U = (1/2)nRT per degree of freedom, and since the temperature is constant, there will be no change in internal energy.
  • #1
TFM
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[SOLVED] Internal Energy of an ideal gas

Homework Statement



The temperature of 0.158 mol of an ideal gas is held constant at 67.0 degrees Celsius while its volume is reduced to a fraction of 20.0 % of its initial volume. The initial pressure of the gas is 1.19 atm.

What is the change in its internal energy?

Homework Equations



[tex] U = \frac{1}{2}nRT [/tex] (Per degrees of Freedom)

The Attempt at a Solution



I tried putting in the values to get U, but it doesn't say how many deggress of Freedom, so I triued using three (Monatomic) But this is wrong. Is there another Formula for the Internal Energy, becasue there are several similar questions, but none seem to be used with the releveant formula above?

So any help/idea will be very greatly appreciated,

TFM
 
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  • #2
hmm U depends only on T, as you can see from the equation.
And In the question, it is mentioned that T is kept constant. (n doesn't change anyway and R is a constant)

so change in U = ??
 
  • #3
As there is no change intemprature, would there be no change in U, then?

TFM
 
  • #4
Yes, if I'm not missing something.

This is valid for ideal gases only, though.
 
  • #5
I just put 0 into MasteringPhysics, and it is the right answer. Thanksm, Raze2Dust! :smile:

Technically, the should the formula actually be:

[tex] U = \frac{1}{2}nR\Delta T [/tex] per degree of Freedom?

Thanks,

TFM
 

1. What is the internal energy of an ideal gas?

The internal energy of an ideal gas refers to the total energy contained within the gas. It includes the kinetic energy of individual gas molecules as well as any potential energy due to intermolecular forces.

2. How is the internal energy of an ideal gas calculated?

The internal energy of an ideal gas can be calculated using the equation U = 3/2 * nRT, where U is the internal energy, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin.

3. What factors affect the internal energy of an ideal gas?

The internal energy of an ideal gas is affected by temperature, pressure, and the number of moles of gas present. Additionally, the type of gas and its specific properties can also impact the internal energy.

4. Is the internal energy of an ideal gas constant?

No, the internal energy of an ideal gas is not constant. It can change as a result of changes in temperature, pressure, or number of moles. However, for an ideal gas, the internal energy remains constant during an isothermal process (a process that occurs at a constant temperature).

5. What is the relationship between internal energy and work done by an ideal gas?

The work done by an ideal gas is equal to the change in internal energy of the gas. This can be expressed as W = ΔU, where W is the work done and ΔU is the change in internal energy. This relationship is known as the first law of thermodynamics.

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