Partition Function Homework: Find Entropy Change for Isothermal Expansion

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In summary, the conversation is about finding the change in entropy of a gas that obeys the van der Waals equation of state when it is isothermally expanded to double its volume. The equation S2-S1=1/T Integral from Vi to 2Vi of PdV is used, but the wrong equation of state is initially used. The correct equation of state is the van der Waals equation.
  • #1
senan
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Homework Statement



One mole of a gas obeys the equation of state
(P +a/V2 )(1 −b/V) =RT/V
Find the change in entropy if one mole of the gas is isothermally expanded until the volume
is doubled. Express your answer in terms of the initial volume of the gas Vi.

Homework Equations



S2-S1=1/T Integral from Vi to 2Vi of PdV

The Attempt at a Solution



I replaced P with P=NkT/V

that leads to

S2-S1=-kln(2Vi/Vi)

as the answer was asked for in terms of Vi I'm not sure that's rightsorry titled the question wrong meant to title other Q as partition function
 
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  • #2
That is not right.

You are using the wrong equation of state.

It is stated in problem that the gas obeys a different equation of state, not the usual, PV=NkT.

You have to use the given equation of state to express P in terms of V.
 
  • #3
By the way, that equation of state is called the van der Waals equation. It takes into account intermolecular forces and the volume of molecules instead of assuming an ideal gas.
 

FAQ: Partition Function Homework: Find Entropy Change for Isothermal Expansion

What is a Partition Function?

A partition function is a mathematical expression that represents the sum of all possible states of a system. It is used in statistical mechanics to calculate the thermodynamic properties of a system, such as entropy and energy.

How is the Partition Function used to calculate entropy change for isothermal expansion?

The partition function is used in the calculation of entropy change for isothermal expansion by taking the natural logarithm of the ratio of the final and initial partition functions. This ratio represents the number of possible states of the system before and after the expansion, and the natural logarithm is used to convert this into a change in entropy.

What is the relationship between entropy change and isothermal expansion?

Entropy change and isothermal expansion are directly related. Isothermal expansion is a process in which a system expands at a constant temperature, and the change in entropy during this process is related to the work done by the system. The higher the entropy change, the more work is done by the system during the expansion.

Can the Partition Function be used for any type of expansion?

No, the partition function is specifically used for calculating entropy change for isothermal expansion. For other types of expansion, such as adiabatic or isobaric, different equations and calculations are used.

Are there any limitations to using the Partition Function to calculate entropy change?

Yes, there are some limitations to using the Partition Function for calculating entropy change. This method assumes that the system is in thermal equilibrium and that all of its energy levels are equally accessible. It also may not be applicable for highly complex systems with numerous interacting particles.

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