Change in Entropy of an expanding gas

In summary: Rln(P2/P1)Since T is constant,ΔS = CVln(Vf/Vi) + CPln(Vf/Vi) + Rln(Pf/Pi)Since it is an ideal gas,CV = 3/2 RCP = 5/2 RSo,ΔS = (3/2 + 5/2) R ln(Vf/Vi) + R ln(Pf/Pi)= 4R ln(Vf/Vi) + R ln(Pf/Pi)= 4R ln(1/2) + R ln(1/2)= -3R ln(2)In summary, the change in entropy of the gas is -
  • #1
Chase11
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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
 
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  • #2
Chase11 said:

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
 
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  • #3
General formula for change in entropy is given as
S2 - S1 = CV[ln(T2 / T1) - ln(V2 / V1)] + CPln(V2/V1)
 

What is entropy?

Entropy is a measure of the amount of disorder or randomness in a system. In thermodynamics, it is often described as the measure of the amount of energy that is unavailable to do work.

How does an expanding gas affect entropy?

When a gas expands, it increases in volume and therefore has more possible microstates (ways in which the molecules can arrange themselves). This increase in disorder leads to an increase in entropy.

What is the relationship between entropy and temperature?

Entropy and temperature have a direct relationship. As temperature increases, the entropy of a system also increases. This is because at higher temperatures, particles have more energy and can move around more freely, increasing disorder and entropy.

How does the change in volume affect the change in entropy of a gas?

The change in volume of a gas has a direct effect on the change in entropy. When a gas expands, the volume increases and the entropy also increases. On the other hand, when a gas is compressed, the volume decreases and the entropy decreases as well.

What is the significance of change in entropy in thermodynamics?

The change in entropy is a fundamental aspect of thermodynamics, as it is a measure of the direction and efficiency of energy transfer in a system. It helps to determine the spontaneity of a process and is crucial in understanding the behavior of gases, liquids, and solids at different temperatures and pressures.

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