Monatomic Gas and Isotherm - W, U Calculations

In summary: Thanks for catching that. I was trying to use \Delta (PV) but got the wrong answer. nC_v/R is the heat transferred per unit volume, right?Yes.
  • #1
dvolpe
37
0

Homework Statement


. Suppose a monatomic ideal gas is changed from state A to state D by one of the processes shown on the PV diagram below, in which each interval on the vertical (P) axis corresponds to 2 atm, and the values of the lines on the horizontal (V) axis equal 1 L, 2 L, and 4 L.

Graph attached.


(a) Find the total work done on the gas if it follows the constant volume path A-B followed by the constant pressure path B-C-D.
(b) Find the total change in internal energy and total heat flow into the gas.

Homework Equations



For isotherm W = nRt (ln (Vf/Vi)
PV = nRT

The Attempt at a Solution



From A to B to C is an isotherm. Use equation above but substitute PV for nRT for either A or C as they are the same - got 255.6 J. Then add in PdeltaV for C to D as on 2 different isotherms. Total work = A to C isotherm work plus C to D work = 655.6. HELP!
 

Attachments

  • New Picture.png
    New Picture.png
    8.1 KB · Views: 1,043
Physics news on Phys.org
  • #2
The path is A-B-C-D. Not sure why you are interested in isotherms. The work from A-B is 0 since there is no change in volume. The work from B-C-D is just the area= P*change in volume. Do you have an correct answer for this problem?
 
  • #3
No. But in a similar problem with intervals on y-axis to be 1 atm and values of lines on x-axis to be 5, 10, and 20 L, the answer is -1520 Joules. I can't get this answer by adding the areas under B-C and C-D to get work (A-B is 0 since it is isochoric). Any ideas?
 
  • #4
Yes you can. Look at the example problem. The area under B-C-D is the work.

Work= P*delta V= (1 atm) *(15 l) (101325 Pa/atm) * (.001 M^3/l)= 1520 J. I am confused why there is a negative work since the change in volume is positive so the work done is positive.
 
  • #5
RTW69 said:
Yes you can. Look at the example problem. The area under B-C-D is the work.

Work= P*delta V= (1 atm) *(15 l) (101325 Pa/atm) * (.001 M^3/l)= 1520 J. I am confused why there is a negative work since the change in volume is positive so the work done is positive.
The work done by the gas would be 1520 J. in that example. But the question asks for the work done ON the gas.

AM
 
  • #6
Thanks..I got the 1520 in that other example by using the 1.013 e 5number to convert (I had used 1.0 e 5 earlier). Now how do I find the internal energy and total heat flow of the total process? I know that change in internal energy = Q-W. If I use change in U = 3/2*nRdeltaT and substitute PV for nRdelta T at each step, I get 3039 J for change in internal energy but that is the answer for total heat flow into the gas. I am confused!
 
  • #7
dvolpe said:
Thanks..I got the 1520 in that other example by using the 1.013 e 5number to convert (I had used 1.0 e 5 earlier). Now how do I find the internal energy and total heat flow of the total process? I know that change in internal energy = Q-W. If I use change in U = 3/2*nRdeltaT and substitute PV for nRdelta T at each step, I get 3039 J for change in internal energy but that is the answer for total heat flow into the gas. I am confused!
Careful:

[tex]\Delta U = nC_v\Delta T = \Delta (PV)C_v/R[/tex]

You appear to be using PV not [itex]\Delta (PV)[/itex].

AM
 
Last edited:

1. What is a monatomic gas?

A monatomic gas is a gas composed of single atoms, such as helium or neon. These atoms do not form molecules and thus have no internal energy due to molecular motion.

2. What is an isotherm?

An isotherm is a graph that represents the relationship between temperature and volume at a constant pressure for a gas. It shows how the volume of a gas changes as the temperature changes while the pressure remains constant.

3. How do you calculate work (W) in a monatomic gas?

Work in a monatomic gas can be calculated using the formula W = PΔV, where P is the pressure and ΔV is the change in volume. This formula assumes that the gas is at a constant pressure.

4. How do you calculate internal energy (U) in a monatomic gas?

Internal energy in a monatomic gas can be calculated using the formula U = (3/2) nRT, where n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin. This formula assumes that the gas is at a constant volume.

5. What is the relationship between work and internal energy in an isothermal process?

In an isothermal process, where the temperature remains constant, the change in internal energy is zero. This means that any work done on or by the gas is equal to the change in internal energy, as represented by the equation W = -U. This is because all the energy transferred to or from the gas is in the form of work, since there is no change in internal energy due to temperature.

Similar threads

  • Introductory Physics Homework Help
Replies
4
Views
818
  • Introductory Physics Homework Help
Replies
33
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
112
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
901
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
754
  • Introductory Physics Homework Help
Replies
3
Views
2K
Replies
11
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
468
Back
Top