What Are the Temperatures of an Ideal Gas During an Adiabatic Expansion?

  • Thread starter Thread starter coldjeanz
  • Start date Start date
  • Tags Tags
    Gas Ideal gas
Click For Summary

Homework Help Overview

The discussion revolves around the adiabatic expansion of a diatomic ideal gas, specifically focusing on determining the initial and final temperatures given certain initial conditions and constraints. The problem involves the application of the ideal gas law and the relationships between pressure, volume, and temperature during the expansion process.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the use of the ideal gas law to find initial and final temperatures, questioning how to resolve the two unknowns without complete information. There are discussions about setting up equations using initial and final values and the implications of using different units in calculations.

Discussion Status

The discussion is ongoing, with participants providing guidance on setting up equations and emphasizing the importance of unit consistency. There is an acknowledgment of confusion regarding the relationship between initial and final temperatures and how to approach solving for them.

Contextual Notes

Participants note the lack of explicit values for the final temperature and the challenges posed by having two unknowns in the equations derived from the ideal gas law. There is a focus on ensuring proper unit usage in calculations.

coldjeanz
Messages
22
Reaction score
0

Homework Statement



A 4.15 mol sample of a diatomic ideal gas (γ = 1.4) expands slowly and adiabatically from a pressure of 5.60 atm and a volume of 13.5 L to a final volume of 34.5 L.

Find initial+final temperatures


Homework Equations



pV/T (all initial) = pV/T (all final)


The Attempt at a Solution



First I was told to solve for the final pressure so I did that easily by doing:

P(final) = P(intial) * (Vi/Vf)^γ

and got 1.5 atm

I am confused on how you find the initial temp if they didn't give the final and vice versa. That's all I really need help with.
 
Physics news on Phys.org
coldjeanz said:
I am confused on how you find the initial temp if they didn't give the final and vice versa. That's all I really need help with.

Use the Ideal Gas Law PV=nRT

ehild
 
Last edited:
But how does that differentiate between the initial and final temp?

P (final-initial) * V (final-initial) = n*R*T(final-initial)

I still have two unknowns then.
 
Two unknowns, two equations.
Read the problem carefully. What is the initial pressure and temperature? What is n, the number of moles? Can you calculate the initial temperature from PV=nRT?

ehild
 
Ok so you set one up using all the initial values and then another using all the final values?

I tried doing this for the initial temp but it's still saying I'm getting the wrong answer...

pV=nRT

(5.6 atm)*(13.5 L) = (4.15 mol)*(8.314 J/mol*K)(T)

I get something like 2.2 and since it wants the answer in K I added 273.15 and I rounded to 276 but it's not right.
 
Without units, the numbers do not mean anything. In what unit is that 2.2? What units do you have to use for the pressure, temperature and volume in the equation

PV=8.314 J/(mol K) n T?

ehild
 

Similar threads

Replies
4
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 33 ·
2
Replies
33
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 9 ·
Replies
9
Views
2K
Replies
5
Views
3K
  • · Replies 8 ·
Replies
8
Views
2K