Change in Entropy of an expanding gas

[Chase11]

Homework Statement

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?

Homework Equations

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

The Attempt at a Solution

I tried using nrTln(vf-vi), but realized I can't 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

 

[Chestermiller]

Homework Statement

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?

Homework Equations

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

The Attempt at a Solution

I tried using nrTln(vf-vi), but realized I can't 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

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

 

[rl.bhat]

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