Calculating the work needed to compress a volume of air

[Minesh]

TL;DR Summary

Need help to figure out the formula for work done for compressing a volume of atm. air using isothermal and polytropic process

Hi All,

I am working on an engineering problem, where i have to calculate the total work needed to compress a volume of air (Locked in a cylindrical chamber similar to an IC chamber where the piston moves to compress the air mixture)

I am defining the process with the below initial parameters,
1. Uncompressed volume of the chamber
2. Compression Ratio
3. States (Pressure and Temperature) before compression corresponds to that of atmospheric values.
4. I assume the process to be a quasi static process

In addition i would also like to know how to add the resistance due to friction of the moving piston into this calculation.

I wanted to know the formula to understand how the work done varies with volume of the air chamber.
Also, i am interested in knowing this from the view of both isothermal and polytropic process.

Thanks a lot in advance

 

[BvU]

Hello Minesh, !

formula for work done for compressing a volume of atm. air using isothermal and polytropic process

4. I assume the process to be a quasi static process

I wanted to know the formula to understand how the work done varies with volume of the air chamber.

You do $$\int p \,dV$$

In addition i would also like to know how to add the resistance due to friction of the moving piston into this calculation.

You add $\int F_\text {friction}\, ds$

 

[Chestermiller]

Summary:: Need help to figure out the formula for work done for compressing a volume of atm. air using isothermal and polytropic process

Hi All,

I am working on an engineering problem, where i have to calculate the total work needed to compress a volume of air (Locked in a cylindrical chamber similar to an IC chamber where the piston moves to compress the air mixture)

I am defining the process with the below initial parameters,
1. Uncompressed volume of the chamber
2. Compression Ratio
3. States (Pressure and Temperature) before compression corresponds to that of atmospheric values.
4. I assume the process to be a quasi static process

In addition i would also like to know how to add the resistance due to friction of the moving piston into this calculation.

I wanted to know the formula to understand how the work done varies with volume of the air chamber.
Also, i am interested in knowing this from the view of both isothermal and polytropic process.

Thanks a lot in advance

What is your approach to this so far?