Ideal gas adiabatic/isovolumetric help

[scholio]

Homework Statement

two moles of an ideal gas is initially at P = 2*20^5 Pa expands adiabaticaly to four times its original volume. it is then compressed at constant pressure to its original volume. what is the change in entropy of the gas

Cp = 20.78 joules/mole-deg
Cv = 12.47 joules/mole-deg
gamma = 5/3

Homework Equations

adiabatic expansion --> PV^gamma = constant, Q = 0
isovolumetric compression --> nCv(deltaT)
entropy deltaS= deltaQ/T

The Attempt at a Solution

i am not sure how to use the adiabatic equation because although P and V is given as well as gamma, i can solve for 'constant' but where does constant come into play?

since for an adiabat Q = 0, do i just take it as zero and move on or do i actually need to solve for something.

as for the isovolumetric compression, moles is given, Cv is given but not deltaT so i solved the Pv=nRT eq for T and subbed it in, i then assumed P and V to be constants as stated in the problem?? and solved for Q getting 1.5 joules

when i solved for entropy i did (compression - expansion, so isovolumetric minus adibat = i subbed in the equation from the isovolumetric equation in and canceled out the T's and was able to get deltaS = 24.94 joules per kelvin

did i take the correct approach? help appreciated...

 

[Chi Meson]

As you have recognized, the heat transferred in an adiabatic process is zero. Therefore, the ratio of Q/T is zero, and there is no change in entropy.

And the second process is at constant pressure (isobaric), not constant volume, so use Cp in the second equation.

You need to find the two temperatures, and for that you need to find the pressure after the adiabatic expansion. That's where the gamma equation comes in. (You said volume is given but you did not state what initial volume is). Once you have the pressure after the expansion, you can get the temperature simply using PV=nRT

Then find the delta T for the isobaric compression.

And to find the delta S, you need a slightly different formula, since T is not constant (look for a natural log formula).

 

[scholio]

hi thanks, just to clarify the problem does not specify an actual volume just the amount at which it decreases/increased