# Work in Adiabatic/ Isothermal and Piston

1. Sep 29, 2011

### ~Sam~

1. The problem statement, all variables and given/known data

Is work greater in adiabatic or isothermal process?

A piston with oxygen has a final volume 1/4 the initial. The temperature is also 5 times greater. Determine pressure change, heat released or absorbed, and work done on or by gas.

2. Relevant equations

the work for adiabatic and isothermal. General w= -integral pdv, conservation of energy deltaV=Q+w

3. The attempt at a solution

I have derived the the expressions for work in both adiabatic and isotherm process from their integrals. ie:- Kln(vf/vi) and -k(vf1-gamma-vi1-gamma)/(1-gamma). But I'm not sure how to show that work in isothermal > adiabatic.

For the second part I'm just not sure how to take into account both temperature and pressure, and I can't assume that it's adiabatic/isothermal in the beginning. Any ideas?

Note: I did trying doing the double integral, dvdt....but i still only get an expression only.

Last edited: Sep 29, 2011
2. Sep 29, 2011

### grzz

Consider a gas undergoing an isothermal and an adiabatic change both having the same change in volume and both starting from the same point on a PV diagram.
Sketching the corresponding PV graphswill show which process has tha bigger work.