Entropy change for isothermal expansion of a perfect gas

In summary, we are asked to calculate the entropy change for an ideal gas at a constant temperature, with 0.85 mol changing its pressure from 350 Torr to 125 Torr. Using the ideal gas law, we can determine that the ratio of the initial volume to the final volume is 2.8. Plugging this into the equation for entropy change, we get a value of 7.276 J/K.
  • #1
Pete_01
51
0

Homework Statement



At a constant temperature, 0.85 mol of an ideal gas changes its pressure from 350 Torr to 125 Torr. Calculate the entropy change for this expansion process.


Homework Equations



Ideal gas: PV=nRT
ΔS = nRln(Vf/Vi)

The Attempt at a Solution



I'm stuck on how to find the volume given the change in pressure, and it being an isothermal process. What am I missing?
 
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  • #2
Since T is constant, so is the righthand side of the ideal gas law. Hence you know that P1V1=P2V2. Note you don't have to find the actual volumes; you just need their ratio.
 
  • #3
vela said:
Since T is constant, so is the righthand side of the ideal gas law. Hence you know that P1V1=P2V2. Note you don't have to find the actual volumes; you just need their ratio.

Ok, perfect thank you. I was wondering if that was how to solve it. So then it would become:

(0.85 mol)(8.314 J/Kmol)ln(2.8) = 7.276 J/K

Correct?
 
  • #4
Looks good. (I'm assuming you have the right equation for the entropy. I don't know them off the top of my head.)
 
  • #5
vela said:
Looks good. (I'm assuming you have the right equation for the entropy. I don't know them off the top of my head.)

Yes, I do. Thanks again!
 

Related to Entropy change for isothermal expansion of a perfect gas

What is entropy change for isothermal expansion of a perfect gas?

The entropy change for isothermal expansion of a perfect gas refers to the change in entropy that occurs when a perfect gas undergoes a process of expansion at a constant temperature.

Why is entropy change important in isothermal expansion of a perfect gas?

Entropy change is important in isothermal expansion of a perfect gas because it allows us to quantify the level of disorder or randomness in the system. This can help us understand the efficiency and thermodynamic behavior of the process.

How is entropy change calculated for isothermal expansion of a perfect gas?

The entropy change for isothermal expansion of a perfect gas can be calculated using the equation ΔS = nRln(V₂/V₁), where ΔS is the change in entropy, n is the number of moles of gas, R is the gas constant, and V₁ and V₂ are the initial and final volumes of the gas.

What factors can affect the entropy change for isothermal expansion of a perfect gas?

The entropy change for isothermal expansion of a perfect gas can be affected by the temperature, the initial and final volumes of the gas, and the number of moles of gas present.

Can the entropy change for isothermal expansion of a perfect gas be negative?

Yes, the entropy change for isothermal expansion of a perfect gas can be negative if the final volume of the gas is smaller than the initial volume. This means that the gas is becoming more ordered and less random, which results in a decrease in entropy.

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