How Do You Calculate Properties of a Gas After Adiabatic Compression?

[swandive76]

Hoping someone can help me here quickly. Trying to get this one question.

a perfect gas is compressed adiabatically from 100 kPa and 17C to a final pressure of 500 kPa and final temp of 77C. The work done during the compression is 45 kJ/kg. Calculate the values of gamma, Cv, R and the molecular weight of the gas.


Please let me know anything you can

Thanks in advance!

Swandive

 

[berkeman]

What are the relevant equations? Can you show us how you think you should approach this problem?

 

[Saketh]

Have you ever derived the expression for adiabatic expansions yourself?

Working from the first law of thermodynamics and an equation of state (the ideal gas law), you should be able to come up with the expressions for work done by a gas in an adiabatic expansion, in addition to expressions for other quantities.

This problem is more of a calculator exercise. I highly recommend that you take the time to derive everything -- suffering through it once will make everything clear in the end. Go over isothermal, isobaric, isochoric, and adiabatic expansions.

You will also find that you will often have to use the ideal gas law to determine unknown initial quantities.

 

[Andrew Mason]

Hoping someone can help me here quickly. Trying to get this one question.

a perfect gas is compressed adiabatically from 100 kPa and 17C to a final pressure of 500 kPa and final temp of 77C. The work done during the compression is 45 kJ/kg. Calculate the values of gamma, Cv, R and the molecular weight of the gas.

Assume this is a reversible adiabatic compression. What is the relationship between P and V in an adiabatic (reversible) change? (hint: it involves $\gamma$)

AM