Change in internal engergy of a monatomic ideal gas

In summary, the problem involves finding the change in internal energy of a monatomic ideal gas that expands at a constant pressure of 2.00 x 10^5 Pa from 1.00 meters cubed to 2.50 meters cubed. To solve for the change in internal energy, we can use the equation \DeltaU = Q + W and calculate work using -P\DeltaV. However, we need to find the energy transferred into the system by heat (Q) which can be calculated using Q = n CpΔT, where Cp = CV + R. With this information, we can solve for the change in internal energy using the equation \DeltaU = 3/2nR\DeltaT
  • #1
alexthelion
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Homework Statement


A monatomic ideal gas expands from 1.00 meters cubed to 2.50 meters cubed at a constant pressure of 2.00 x 10^5 Pa. Find the change in the internal energy of the gas.



Homework Equations



[tex]\Delta[/tex]U = Q + W

The Attempt at a Solution



Well, I know how to find work, which is -P[tex]\Delta[/tex]V

But I'm having trouble finding the energy transferred into the system by heat, or Q, because the problem does not give a specific value for it.

I would much appreciate it if someone could give me some pointers as to how to find Q.
 
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  • #2
How is Q related the the specific heat at constant pressure?
 
  • #3
I don't exactly know, I do know that [tex]\Delta[/tex]U = 3/2nR[tex]\Delta[/tex]T for a monatomic gas, where the molar specific heat is given by Cv = 3/2R
 
  • #4
If you know CV, then Cp = CV + R. Also at constant pressure Q = n CpΔT. Now you can put it together.
 
  • #5
Aha, thanks for the help! I got it.
 

What is internal energy?

Internal energy refers to the total energy present in a system, including both its kinetic and potential energy. In the context of a monatomic ideal gas, it primarily refers to the kinetic energy of the gas particles.

What factors affect the change in internal energy of a monatomic ideal gas?

The change in internal energy of a monatomic ideal gas is affected by several factors, including temperature, pressure, and volume. It follows the first law of thermodynamics, which states that the change in internal energy is equal to the heat added to the system minus the work done by the system.

What is the equation for calculating the change in internal energy of a monatomic ideal gas?

The change in internal energy (ΔU) of a monatomic ideal gas can be calculated using the equation ΔU = (3/2) nRΔT, where n is the number of moles of gas, R is the gas constant, and ΔT is the change in temperature.

Can the change in internal energy of a monatomic ideal gas be negative?

Yes, the change in internal energy of a monatomic ideal gas can be negative if the gas loses heat or does work on its surroundings. In this case, the internal energy of the gas decreases, resulting in a negative value for ΔU.

How does the change in internal energy affect the thermodynamic properties of a monatomic ideal gas?

The change in internal energy plays a significant role in determining the thermodynamic properties of a monatomic ideal gas, such as its temperature, pressure, and volume. It is also closely related to the gas's enthalpy, which is a measure of its heat content. Changes in internal energy can lead to changes in these properties, which can have important implications in various scientific and industrial applications.

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