Calculating Work in an Adiabatic Process for a Diatomic Gas

In summary, To find the work done in compressing 5.00 mol of O2 at 20.0 Celsius and 1.00atm to 1/10 the original volume, we can use the ideal gas law (PV = nRT) to solve for the initial condition. Then, we can use the equation W=\int_{V1}^{V2}PdV and the fact that Q=0 for an adiabatic process to find the work done (L=-\nu C_V \Delta T). The final temperature can be found using the equation TV^{\gamma-1}=const and the gas's specific heat capacity. It should be noted that the work done by the gas in
  • #1
sisigsarap
17
0
I have 5.00 mol of O2(Oxygen) at 20.0 Celsius and 1.00atm. I will compress this to 1/10 the original volume.

Find the work? The correct answer is 46.1 Kj

I am having a terrible time with this.

This is what I know: Q = 0 for an adiabatic process, and the change in internal energy is equal to work.

I think I use integrate Pdv, but I am getting very confused. I am really lost and need a push in the right direction!
 
Physics news on Phys.org
  • #2
Ideal gas law? You know pressure, temperature and the number of atoms and 1 atm is much less than the critical pressure.
 
  • #3
PV = nRT
I just don't see how to plug it in. Pleaseee help its driving me crazy!
 
  • #4
sisigsarap said:
PV = nRT
I just don't see how to plug it in. Pleaseee help its driving me crazy!

What variable do you not have a value for? There's only one. Solve for the unknown plug in your known values. This will yield your initial condition. Apply the condition in the question. Then use:

[tex]W=\int_{V1}^{V2}PdV[/tex]
 
  • #5
In an adiabatic process [tex]Q=0[/tex] then [tex]\Delta U+L=0[/tex] and [tex]L=-\Delta U[/tex]. You can find now
[tex]L=-\nu C_V \Delta T[/tex].
(Because you deal with a diatomic gas, you'll have [tex]C_V=\frac{5}{2}R[/tex]).

The final temperature is taken from [tex]TV^{\gamma-1}=const[/tex] (here [tex]T[/tex] is in Kelvin, as you probably know).

OBS. In my opinion, the work made by the gas must be negative!
 
Last edited:

1. What is an adiabatic process?

An adiabatic process is a thermodynamic process in which there is no transfer of heat or matter between a system and its surroundings. This means that the system is insulated and does not exchange energy with its environment.

2. How is work related to adiabatic processes?

In an adiabatic process, work is done on or by the system in order to change its state. This work is usually in the form of compression or expansion of a gas, and it is necessary to maintain the internal energy of the system.

3. What factors affect the work done in an adiabatic process?

The work done in an adiabatic process is affected by the initial and final states of the system, the type of gas, and the rate at which the process occurs. It is also dependent on the external pressure and volume of the system.

4. What is the formula for calculating work in an adiabatic process?

The formula for work in an adiabatic process is W = -PΔV, where W is work, P is external pressure, and ΔV is the change in volume of the system.

5. How is an adiabatic process different from an isothermal process?

An adiabatic process is different from an isothermal process in that it does not involve any heat exchange with the surroundings, whereas an isothermal process maintains a constant temperature by exchanging heat with the surroundings. Additionally, the work done in an adiabatic process is usually greater than that in an isothermal process.

Similar threads

  • Introductory Physics Homework Help
Replies
19
Views
1K
  • Introductory Physics Homework Help
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
773
  • Introductory Physics Homework Help
Replies
8
Views
665
  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
25
Views
3K
Replies
22
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
3K
Back
Top