# Change in Entropy of an expanding gas

1. Apr 17, 2014

### Chase11

1. The problem statement, all variables and given/known data
Four moles of an ideal gas expands at constant temperature until its pressure is reduced to half of its initial value. What is the change in entropy of the gas?

2. Relevant equations
ΔS=Q/T (For constant T) pinitial=p pfinal=.5p
Q=W
W=pdv
nrTln(vf/vi)

3. The attempt at a solution
I tried using nrTln(vf-vi), but realized I cant do that not knowing the temperature or the volumes. Is there an equation using deltap that I could use to solve for this that I am unaware of or can't figure out? Thanks

2. Apr 17, 2014

### Staff: Mentor

The problem statement says the the temperature is constant. So PV= constant. So, if you know the ratio of the initial and final pressures, you also know the ratio of the initial and final volumes. Please note also that you have implicitly assumed that the expansion is reversible.

Chet

3. Apr 17, 2014

### rl.bhat

General formula for change in entropy is given as
S2 - S1 = CV[ln(T2 / T1) - ln(V2 / V1)] + CPln(V2/V1)