How Is Work Calculated in Isothermal Compression of Air?

Click For Summary
SUMMARY

The work done in isothermal compression of 2 kg of dry air to one-tenth its volume at 15°C can be calculated using the integral of pressure times the change in volume. The equation does not include a variable for the mass of the air parcel, indicating that the solution can be expressed in terms of pressure (p) as a variable. This approach allows for a general solution that remains valid despite unknown parameters. The integral should be set up with limits corresponding to the initial and final volumes, v1 and v2.

PREREQUISITES
  • Understanding of thermodynamics principles, specifically isothermal processes
  • Familiarity with calculus, particularly integration techniques
  • Knowledge of the ideal gas law and its application to air
  • Basic concepts of pressure-volume work in thermodynamic systems
NEXT STEPS
  • Study the ideal gas law and its implications for air compression
  • Learn about the derivation and application of the work integral in thermodynamics
  • Explore isothermal processes in greater detail, including real-world applications
  • Investigate the effects of temperature on gas behavior during compression
USEFUL FOR

Students and professionals in mechanical engineering, thermodynamics researchers, and anyone involved in the study of gas compression processes.

icnhoj
Messages
1
Reaction score
0
1. Calculate the work done in compressing isothermally 2kg of dry air to one-tenth its volume at 15C



2. Work= the integral of pressure times the change in volume, the limits of integration being the initial and final volumes, v1 and v2.



3. The equation is very general, and doesn't have a variable for mass of the air parcel. The problem also doesn't have a value for p, so I don't know if I am supposed to have a solution with p as a variable in it...
 
Physics news on Phys.org
Just set up the integral leaving variables where you don't know something. You may find the answer doesn't depend on things you don't know.
 

Similar threads

Adiabatic Expansion of Pressurized Air in a Piston-Cylinder Setup
  • · Replies 8 ·
Replies
8
Views
2K
Efficiency of Stirling Cycle - Is it the same as the Carnot Engine?
  • · Replies 14 ·
Replies
14
Views
2K
Calculate Work (w) for Isothermal Gas Expansion/Compression
  • · Replies 4 ·
Replies
4
Views
2K
To find total work done from multiple reversible processes
  • · Replies 3 ·
Replies
3
Views
2K
Work done in adiabatic process vs work done in isothermal
  • · Replies 2 ·
Replies
2
Views
3K
Is My Calculation for Bicycle Pump Pressure Incorrect?
  • · Replies 116 ·
4
Replies
116
Views
7K
Trouble solving for end state of two control volumes in a rigid tank
  • · Replies 12 ·
Replies
12
Views
2K
Thermodynamics Work from pressure
  • · Replies 4 ·
Replies
4
Views
2K
How Is Work Calculated for a Gas and Balloon in Isothermal Expansion?
  • · Replies 11 ·
Replies
11
Views
5K
Which Gas Compression Process Requires the Most Work?
  • · Replies 1 ·
Replies
1
Views
3K