Adiabatic process thermodynamics help

Click For Summary
SUMMARY

The discussion focuses on solving an adiabatic process problem involving an ideal diatomic gas compressed to 40% of its original volume at an initial temperature of 75 K. The key equations utilized include the first law of thermodynamics (delta U = Q - W), the adiabatic condition (PVγ = constant), and the derived relationship (TVγ-1 = constant). The final temperature can be determined using these equations without needing the pressure, as Q equals zero in an adiabatic process.

PREREQUISITES
  • Understanding of the first law of thermodynamics
  • Familiarity with adiabatic processes in thermodynamics
  • Knowledge of ideal gas laws and properties
  • Ability to manipulate equations involving constants and variables
NEXT STEPS
  • Study the derivation of the adiabatic equation TVγ-1 = constant
  • Learn about the specific heat ratio (γ) for diatomic gases
  • Explore practical applications of adiabatic processes in thermodynamics
  • Practice solving problems involving adiabatic compression and expansion
USEFUL FOR

Students studying thermodynamics, particularly those focusing on gas laws and adiabatic processes, as well as educators looking for problem-solving strategies in physics and engineering contexts.

uchicago2012
Messages
74
Reaction score
0

Homework Statement


An ideal diatomic gas at 75 K is adiabatically compressed to 40% its original volume. What is its final temperature?

Homework Equations


delta U = Q - W
W = the integral of PdV
PVgamma = constant
U = 5/2nKT = 5/2nRT (diatomic, ideal gas)

The Attempt at a Solution


So I'm having trouble because I don't know the pressure. I'm sure you can solve it without the pressure, but I didn't really see how to. Since it's an adiabatic process, Q= 0 so delta U = -W. I tried to write equations separately for U and W and set them equal to the negative of one another, but that ended badly, since the two equations were almost identical and everything, including my final temperature, divides out. Also, I wasn't sure if I can just solve for the problem using 1 mole as the amount present, but that's what I tried to do.
 
Physics news on Phys.org


You need the form of the adiabatic equation with T and V in it.
Do you have this in your notes or book?
It is derived by combining the one you mention, pVγ = constant, with pV/T = constant. [by division of one by the other to eliminate p]
 


uchicago2012 said:
PVγ = constant

Since you know this equation, you should probably know this one, too:

TVγ-1 = constant.

And you should know (or at least have in your textbook) the value of γ. Therefore, you can solve this problem fairly easily.
 

Similar threads

Help Calculate Work Done in Adiabatic Process & Fill Table
  • · Replies 19 ·
Replies
19
Views
2K
Thermally insulated container with alternating series of walls
  • · Replies 49 ·
2
Replies
49
Views
4K
How to calculate initial pressure and temperature - adiabatic process
  • · Replies 7 ·
Replies
7
Views
2K
Correct Derivation of the Adiabatic Condition? (PV Diagram)
  • · Replies 4 ·
Replies
4
Views
1K
Thermodynamic cyclic process - 2 isobaric and 2 adiabatic
  • · Replies 5 ·
Replies
5
Views
1K
When do formulas for adiabatic processes apply?
  • · Replies 1 ·
Replies
1
Views
1K
Work done in adiabatic process vs work done in isothermal
  • · Replies 2 ·
Replies
2
Views
3K
Adiabatic expansion with temperature-dependent gamma
  • · Replies 1 ·
Replies
1
Views
2K
Adiabatic Expansion of Pressurized Air in a Piston-Cylinder Setup
  • · Replies 8 ·
Replies
8
Views
2K
Thermodynamics Problem: Reversible and Irreversible Processes
  • · Replies 1 ·
Replies
1
Views
2K