How Does Pressure Change Affect Internal Energy in an Ideal Gas?

In summary: In the first equation, you are finding the change in internal energy from state A to state D. In the second equation, you are finding the change in internal energy from state E to state D.In summary, the data in the problem is inconsistent and it is unclear what formula you are using.
  • #1
hockeyfan123
1
0
Homework Statement
Monoatomic ideal gas question
Relevant Equations
Internal Energy
Screen Shot 2022-12-04 at 4.14.28 PM.png


P1=1.9 and P2=4.8.

Question: what is the total change in internal energy

This is what I have so far but it is still incorrect I believe:

U= (3/2)(1/2)(2.9)(1.01x10^3)(8x10^-3)

Where am I going wrong?
 
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  • #2
hockeyfan123 said:
Homework Statement:: Monoatomic ideal gas question
Relevant Equations:: Internal Energy

View attachment 318195

P1=1.9 and P2=4.8.

Question: what is the total change in internal energy

This is what I have so far but it is still incorrect I believe:

U= (3/2)(1/2)(2.9)(1.01x10^3)(8x10^-3)

Where am I going wrong?
Hello and welcome to PF!

It's not clear what formula you are using. You did not list the formula in the "Relevant Equations" section. Also, it would be good to include the units with your numerical values.

It appears to me that the data given in the problem is inconsistent. The change in internal energy should not depend on the particular path going from state A to state D. But I find different changes in energy for different paths.
 
  • #3
I don't quite understand this equation
hockeyfan123 said:
U= (3/2)(1/2)(2.9)(1.01x10^3)(8x10^-3)
Please write symbolically first then show the numbers that you substitute. You can post equations in LateX. Click on the link "LaTeX guide", lower left, to learn how.

One wrong thing is that your answer is an internal energy at some point, not clear which. You are supposed to find the change in internal energy from A to D. This means the difference ##U_D-U_A##.
 
  • #4
Another way to see that the data is inconsistent is to consider states E and D. They are at the same temperature. State E has half the volume of state D. Therefore, from Boyles's law (or from PV = nRT), state E should have twice the pressure of state D. But ##P_D## is given to be 1.9 atm and ##P_E## is given to be 4.8 atm. Check to see if the 4.8 atm was actually given as 3.8 atm.
 
  • #5
The two equations you should be working with are $$\Delta U=nC_v\Delta T$$ and $$\Delta (PV)=nR\Delta T$$
 

Related to How Does Pressure Change Affect Internal Energy in an Ideal Gas?

1. What is a monatomic ideal gas?

A monatomic ideal gas is a theoretical model of a gas made up of particles that are considered to be point masses with no internal structure. This means that the particles do not have any rotational or vibrational energy, and they do not interact with each other except through collisions.

2. How is a monatomic ideal gas different from a real gas?

In reality, most gases are not monatomic and have more complex structures, such as diatomic or polyatomic molecules. These molecules have internal energy and can interact with each other through intermolecular forces, making them behave differently than a monatomic ideal gas.

3. What is the ideal gas law and how does it apply to monatomic ideal gases?

The ideal gas law is a mathematical relationship between the pressure, volume, temperature, and number of moles of a gas. It states that for any ideal gas, the product of its pressure and volume is directly proportional to its temperature and number of moles. This law applies to monatomic ideal gases because they follow the assumptions of the ideal gas model.

4. What are some real-world applications of the monatomic ideal gas model?

The monatomic ideal gas model is used in many branches of science, including chemistry, physics, and engineering. It is commonly used to study and predict the behavior of gases in various systems, such as in chemical reactions, gas laws, and thermodynamics.

5. Are there any limitations to the monatomic ideal gas model?

Yes, there are several limitations to the monatomic ideal gas model. It assumes that the gas particles have no volume, which is not true for real gases. It also does not take into account intermolecular forces, which can affect the behavior of gases at high pressures or low temperatures. Additionally, the model does not consider the effects of quantum mechanics, which become important at very low temperatures.

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