- The equation of state of the hard sphere gas

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# The equation of state of the hard sphere gas

Author

Goh, Li Li

Supervisor

Shutler, Paul

Abstract

Carnahan & Starling (C-S) (1969) approximated the equation of state of hard sphere gas to be :

where η = packing fraction of molecules in the gas

N = number of hard spheres in volume V at temp T and pressure P

By comparison with Alder's & Wainwright's (A&W) (1960) molecular dynamics data, which is collected based on the simulation of moving hard spheres, C-S's Z is a good approximation within 1.5 % of A&W's molecular dynamics data.

This research concentrates on verifying the accuracy of C-S approximation to the equation of state of hard sphere gas by simulating stationary molecules on FORTRAN 77. By computing the interstitial volume Vinter of random configuration of spheres for each simulation, the computer's calculated. This f(η) is compared with C-S's equivalent f(η), which is derived to be:

The computer output is well approximated by C-S's equivalent f(η), indicating that C-S's approximation to Z is good, as expected. Because these hard spheres are non-attracting, Z is logically equivalent to f However, the latter approach is much easier to model on a computer as only stationary molecules are considered.

where η = packing fraction of molecules in the gas

N = number of hard spheres in volume V at temp T and pressure P

By comparison with Alder's & Wainwright's (A&W) (1960) molecular dynamics data, which is collected based on the simulation of moving hard spheres, C-S's Z is a good approximation within 1.5 % of A&W's molecular dynamics data.

This research concentrates on verifying the accuracy of C-S approximation to the equation of state of hard sphere gas by simulating stationary molecules on FORTRAN 77. By computing the interstitial volume Vinter of random configuration of spheres for each simulation, the computer's calculated. This f(η) is compared with C-S's equivalent f(η), which is derived to be:

The computer output is well approximated by C-S's equivalent f(η), indicating that C-S's approximation to Z is good, as expected. Because these hard spheres are non-attracting, Z is logically equivalent to f However, the latter approach is much easier to model on a computer as only stationary molecules are considered.

Date Issued

1997

Call Number

QA166.7 Goh

Date Submitted

1997