.MCAD 303010000 1 74 75 0
.CMD PLOTFORMAT
0 0 1 1 0 0 1 
0 0 1 1 0 0 1 
0 1 0 0 NO-TRACE-STRING
0 2 1 0 NO-TRACE-STRING
0 3 2 0 NO-TRACE-STRING
0 4 3 0 NO-TRACE-STRING
0 1 4 0 NO-TRACE-STRING
0 2 5 0 NO-TRACE-STRING
0 3 6 0 NO-TRACE-STRING
0 4 0 0 NO-TRACE-STRING
0 1 1 0 NO-TRACE-STRING
0 2 2 0 NO-TRACE-STRING
0 3 3 0 NO-TRACE-STRING
0 4 4 0 NO-TRACE-STRING
0 1 5 0 NO-TRACE-STRING
0 2 6 0 NO-TRACE-STRING
0 3 0 0 NO-TRACE-STRING
0 4 1 0 NO-TRACE-STRING
0 1 21 15 0 3 
.CMD FORMAT  rd=d ct=10 im=i et=3 zt=15 pr=3 mass length time charge temperature tr=0 vm=0
.CMD SET ORIGIN 0
.CMD SET TOL 0.001000000000000
.CMD SET PRNCOLWIDTH 8
.CMD SET PRNPRECISION 4
.CMD PRINT_SETUP 1.200000 1.218750 1.200000 1.200000 0
.CMD HEADER_FOOTER 1 1 *empty* *empty* *empty* 0 1 *empty* *empty* *empty*
.CMD HEADER_FOOTER_FONT fontID=14 family=Arial points=10 bold=0 italic=0 underline=0
.CMD HEADER_FOOTER_FONT fontID=15 family=Arial points=10 bold=0 italic=0 underline=0
.CMD DEFINE_FONTSTYLE_NAME fontID=0 name=Variables
.CMD DEFINE_FONTSTYLE_NAME fontID=1 name=Constants
.CMD DEFINE_FONTSTYLE_NAME fontID=2 name=Text
.CMD DEFINE_FONTSTYLE_NAME fontID=4 name=User^1
.CMD DEFINE_FONTSTYLE_NAME fontID=5 name=User^2
.CMD DEFINE_FONTSTYLE_NAME fontID=6 name=User^3
.CMD DEFINE_FONTSTYLE_NAME fontID=7 name=User^4
.CMD DEFINE_FONTSTYLE_NAME fontID=8 name=User^5
.CMD DEFINE_FONTSTYLE_NAME fontID=9 name=User^6
.CMD DEFINE_FONTSTYLE_NAME fontID=10 name=User^7
.CMD DEFINE_FONTSTYLE fontID=0 family=Times^New^Roman points=10 bold=0 italic=0 underline=0
.CMD DEFINE_FONTSTYLE fontID=1 family=Times^New^Roman points=10 bold=0 italic=0 underline=0
.CMD DEFINE_FONTSTYLE fontID=2 family=Arial points=10 bold=0 italic=0 underline=0
.CMD DEFINE_FONTSTYLE fontID=4 family=Arial points=10 bold=0 italic=0 underline=0
.CMD DEFINE_FONTSTYLE fontID=5 family=Courier^New points=10 bold=0 italic=0 underline=0
.CMD DEFINE_FONTSTYLE fontID=6 family=System points=10 bold=0 italic=0 underline=0
.CMD DEFINE_FONTSTYLE fontID=7 family=Script points=10 bold=0 italic=0 underline=0
.CMD DEFINE_FONTSTYLE fontID=8 family=Roman points=10 bold=0 italic=0 underline=0
.CMD DEFINE_FONTSTYLE fontID=9 family=Modern points=10 bold=0 italic=0 underline=0
.CMD DEFINE_FONTSTYLE fontID=10 family=Times^New^Roman points=10 bold=0 italic=0 underline=0
.CMD UNITS U=1
.CMD DIMENSIONS_ANALYSIS 0 0
.TXT 6 1 1 0
Cg a73.250000,73.000000,251
{\rtf1\ansi \deff1
{\fonttbl
{\f0\fnil Symbol;}
{\f1\fnil Arial;}
}
{\plain {The hard sphere model is a popular
 starting point for building theoretical
 models of equations of states for fluids.
 }{The following equation, due to Carnahan
 and Starling, is a good approximation to
 the equation of state for a hard sphere
 fluid:}}
}
.EQN 8 19 2 0
({0:P}NAME*{0:V}NAME)/({0:N}NAME*{0:k}NAME*{0:T}NAME)
.TXT 0 7 4 0
Cg a1.000000,56.000000,4
{\rtf1\ansi \deff1
{\fonttbl
{\f0\fnil Symbol;}
{\f1\fnil Arial;}
}
{\plain {=}}
}
.EQN 0 3 5 0
(1+{0:y}NAME+({0:y}NAME)^(2)-({0:y}NAME)^(3))/(((1-{0:y}NAME))^(3))
.TXT 4 -29 7 0
Cg a4.250000,73.000000,8
{\rtf1\ansi \deff1
{\fonttbl
{\f0\fnil Symbol;}
{\f1\fnil Arial;}
}
{\plain {where}}
}
.EQN 2 11 8 0
{0:y}NAME
.TXT 0 4 9 0
Cg a1.000000,58.000000,4
{\rtf1\ansi \deff1
{\fonttbl
{\f0\fnil Symbol;}
{\f1\fnil Arial;}
}
{\plain {=}}
}
.EQN 0 4 10 0
({0:\p}NAME*{0:N}NAME*({0:d}NAME)^(3))/(6*{0:V}NAME)
.TXT 4 -19 12 0
Cg a68.125000,73.000000,387
{\rtf1\ansi \deff1
{\fonttbl
{\f0\fnil Symbol;}
{\f1\fnil Arial;}
}
{\plain {(a) Plot the compressibility, z
 = PV/NkT of this fluid as a function of
 y. \par (b) Also plot z versus v = V/(Nk),
 assuming the value d = 3.00x10}{\fs16 \up6 
-10}{ m. \par (c) Also plot the compressibility
 versus volume for this gas and compare 
with the simpler ideal equation with excluded
 volume: P=RT/(V-b).\par *****************************************************************************
 }}
}
.TXT 12 0 75 0
Cg a1.875000,73.000000,4
{\rtf1\ansi \deff1
{\fonttbl
{\f0\fnil Symbol;}
{\f1\fnil Arial;}
}
{\plain (a)}
}
.EQN 0 5 16 0
{0:y}NAME:0,.01;.90
.EQN 1 -5 14 0
&&(_n_u_l_l_&_n_u_l_l_)&(1+{0:y}NAME+({0:y}NAME)^(2)-({0:y}NAME)^(3))/(((1-{0:y}NAME))^(3))@&&(_n_u_l_l_&_n_u_l_l_)&{0:y}NAME
0 0 1 1 0 0 1 
0 0 1 1 0 0 1 
0 1 0 0 NO-TRACE-STRING
0 2 1 0 NO-TRACE-STRING
0 3 2 0 NO-TRACE-STRING
0 4 3 0 NO-TRACE-STRING
0 1 4 0 NO-TRACE-STRING
0 2 5 0 NO-TRACE-STRING
0 3 6 0 NO-TRACE-STRING
0 4 0 0 NO-TRACE-STRING
0 1 1 0 NO-TRACE-STRING
0 2 2 0 NO-TRACE-STRING
0 3 3 0 NO-TRACE-STRING
0 4 4 0 NO-TRACE-STRING
0 1 5 0 NO-TRACE-STRING
0 2 6 0 NO-TRACE-STRING
0 3 0 0 NO-TRACE-STRING
0 4 1 0 NO-TRACE-STRING
0 1 48 21 0 3 
.TXT 32 1 22 0
Cg a26.250000,71.000000,41
{\rtf1\ansi \deff1
{\fonttbl
{\f0\fnil Symbol;}
{\f1\fnil Arial;}
}
{\plain (b) {Substitute for y in the expression}}
}
.EQN 0 32 17 0
(1+{0:y}NAME+({0:y}NAME)^(2)-({0:y}NAME)^(3))/(((1-{0:y}NAME))^(3))
.TXT 11 -32 23 0
Cg a16.125000,71.000000,26
{\rtf1\ansi \deff1
{\fonttbl
{\f0\fnil Symbol;}
{\f1\fnil Arial;}
}
{\plain {And simplify the result}}
}
.EQN 0 28 20 0
((1+(1)/(6)*{0:\p}NAME*{0:N}NAME*(({0:d}NAME)^(3))/({0:V}NAME)+(1)/(36)*({0:\p}NAME)^(2)*({0:N}NAME)^(2)*(({0:d}NAME)^(6))/(({0:V}NAME)^(2))-(1)/(216)*({0:\p}NAME)^(3)*({0:N}NAME)^(3)*(({0:d}NAME)^(9))/(({0:V}NAME)^(3))))/(((1-(1)/(6)*{0:\p}NAME*{0:N}NAME
*(({0:d}NAME)^(3))/({0:V}NAME)))^(3))
.TXT 12 -29 24 0
Cg a6.250000,72.000000,12
{\rtf1\ansi \deff1
{\fonttbl
{\f0\fnil Symbol;}
{\f1\fnil Arial;}
}
{\plain {to obtain}}
}
.EQN 0 29 63 0
((({0:V}NAME)^(3)+({0:\p}NAME)/(6)*{0:N}NAME*({0:d}NAME)^(3)*({0:V}NAME)^(2)+((({0:\p}NAME)/(6)))^(2)*({0:N}NAME)^(2)*({0:d}NAME)^(6)*{0:V}NAME-((({0:\p}NAME)/(6)))^(3)*({0:N}NAME)^(3)*({0:d}NAME)^(9)))/((({0:V}NAME-({0:\p}NAME)/(6)*{0:N}NAME*({0:d}NAME)^
(3)))^(3))
.TXT 15 -29 66 0
Cg a10.000000,72.000000,18
{\rtf1\ansi \deff1
{\fonttbl
{\f0\fnil Symbol;}
{\f1\fnil Arial;}
}
{\plain (c) {So, let b =}}
}
.EQN 0 11 69 0
({0:\p}NAME)/(6)*{0:N}NAME*({0:d}NAME)^(3)
.TXT 0 12 73 0
Cg a22.750000,54.000000,33
{\rtf1\ansi \deff1
{\fonttbl
{\f0\fnil Symbol;}
{\f1\fnil Arial;}
}
{\plain {recognise the excluded volume.}}
}
.EQN 0 25 71 0
((({0:V}NAME)^(3)+{0:b}NAME*({0:V}NAME)^(2)+({0:b}NAME)^(2)*{0:V}NAME-({0:b}NAME)^(3)))/((({0:V}NAME-{0:b}NAME))^(3))
.EQN 9 -48 25 0
{0:N}NAME:6.022*(10)^(23)
.EQN 0 15 26 0
{0:d}NAME:3.0*(10)^(-10)*{0:m}NAME
.EQN 0 17 29 0
{0:V}NAME:0.03*({0:dm}NAME)^(3),.035*({0:dm}NAME)^(3);0.5*({0:dm}NAME)^(3)
.EQN 0 25 67 0
{0:b}NAME:({0:\p}NAME)/(6)*{0:N}NAME*({0:d}NAME)^(3)
.EQN 4 -57 27 0
&&(_n_u_l_l_&_n_u_l_l_)&(({0:V}NAME)^(3)+{0:b}NAME*({0:V}NAME)^(2)+({0:b}NAME)^(2)*{0:V}NAME-({0:b}NAME)^(3))/((({0:V}NAME-{0:b}NAME))^(3)),({0:V}NAME)/({0:V}NAME-{0:b}NAME)@&&(_n_u_l_l_&_n_u_l_l_)&({0:V}NAME)/(({0:dm}NAME)^(3))
0 0 1 1 0 0 1 
0 0 1 1 0 0 1 
0 1 0 0 NO-TRACE-STRING
0 2 1 0 NO-TRACE-STRING
0 3 2 0 NO-TRACE-STRING
0 4 3 0 NO-TRACE-STRING
0 1 4 0 NO-TRACE-STRING
0 2 5 0 NO-TRACE-STRING
0 3 6 0 NO-TRACE-STRING
0 4 0 0 NO-TRACE-STRING
0 1 1 0 NO-TRACE-STRING
0 2 2 0 NO-TRACE-STRING
0 3 3 0 NO-TRACE-STRING
0 4 4 0 NO-TRACE-STRING
0 1 5 0 NO-TRACE-STRING
0 2 6 0 NO-TRACE-STRING
0 3 0 0 NO-TRACE-STRING
0 4 1 0 NO-TRACE-STRING
0 1 33 28 0 3 
.TXT 43 0 74 0
Cg a72.000000,72.000000,146
{\rtf1\ansi \deff1
{\fonttbl
{\f0\fnil Symbol;}
{\f1\fnil Arial;}
}
{\plain {The Carnahan and Starling model
 shows a much higher compressibility at 
small volumes than does the simpler excluded
 volume modified ideal gas.}}
}
.EQN 24 0 30 0
{0:dm}NAME~({0:m}NAME)/(10)