initial commit / add all books

11 files changed, 278 insertions, 0 deletions

diff --git a/1919/CH11/EX11.1/Ex11_1.sce b/1919/CH11/EX11.1/Ex11_1.sce
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+

+// Theory and Problems of Thermodynamics

+// Chapter 11

+// Kinetic Theory of Gases

+// Example 1

+clear ;clc;

+

+//Given data

+phi = 30               // phi lies between 29.5 and 30.5

+theta = 45             // theta lies between 44.5 and 45.5

+

+// Calculations

+// fraction of gas having velocities ia given by

+// dn_p_t/n = 1/4/%pi*sin(theta)dt*dp       where t=theta; p=phi

+// since dt and dp are small values , above equation can be written in the 

+// differnt form as

+// dn_p_t/n = 1/4/%pi*sin(theta)*del_t*del_p

+

+del_t = %pi/180             // in radians for 1 degree

+del_p = %pi/180             // in radians for 1 degree

+theta = 45 * del_t          // in radians

+

+f = 1/(4*%pi)*sin(theta)*del_t*del_p

+

+

+// output results

+mprintf('fraction of gas having velocities = %4.3f E-05', f*1e5)

diff --git a/1919/CH11/EX11.10/Ex11_10.sce b/1919/CH11/EX11.10/Ex11_10.sce
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index 000000000..43b4ffbcb
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+

+// Theory and Problems of Thermodynamics

+// Chapter 11

+// Kinetic Theory of Gases

+// Example 10

+

+clear ;clc;

+

+//Given data

+r1 = 0.18               // radius of oxygen molecule in nm

+P = 0.01                // pressure of oxygen in MPa

+T = 500                 // temperature of oxygen in K

+R = 8.314               // gas constant

+N0 = 6.023*1e23         // number of atoms per mole

+M = 32*1e-3             // molar mass of oxygen in kg/mol

+

+// Calculations

+sig = 4*%pi*((r1*1e-9)^2)   // collision cross section

+

+n = P*N0/(R*T)              // molecules per m^3

+

+lam = 1/(sig*n)             // mean free path

+

+X1 = exp(-1.5/lam)          // fraction of free paths longer than 1.5m

+X2 = 1- X1                  // fraction of free paths shorter than 1.5m

+X3 = 1- exp(-2/lam)            // fraction of free paths shorter than 2m

+

+r_f = X3 - X2               // fraction between 1.5 and 2 m

+

+// output results

+mprintf('(a) Fraction of free paths longer than 1.5 m = %4.4f ', X1)

+mprintf('\n (b) Fraction of free paths longer than 1.5 m but shorter than 2 m = %4.4f ', r_f)

diff --git a/1919/CH11/EX11.11/Ex11_11.sce b/1919/CH11/EX11.11/Ex11_11.sce
new file mode 100755
index 000000000..cbdb095b7
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+

+// Theory and Problems of Thermodynamics

+// Chapter 11

+// Kinetic Theory of Gases

+// Example 11

+

+clear ;clc;

+

+//Given data

+T = 273                 // temperature of oxygen in K

+vis =19.2               // viscosity of oxygen 

+R = 8.314               // gas constant

+N0 = 6.023*1e23         // number of atoms per mole

+M = 32*1e-3             // molar mass of oxygen in kg/mol

+

+// Calculations

+V = (8*R*T/(%pi*M))^0.5         // average velocity of gas molecule

+

+sig = M*V/(N0*vis*(1e-6)*3*(2^0.5))

+

+//sig = 4*%pi*r1^2

+r1 = (sig/(4*%pi))^0.5

+

+// output results

+mprintf('Hard sphere radius of oxygen molecule = %4.2f nm', r1*1e9)

diff --git a/1919/CH11/EX11.2/Ex11_2.sce b/1919/CH11/EX11.2/Ex11_2.sce
new file mode 100755
index 000000000..326d2e131
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+++ b/1919/CH11/EX11.2/Ex11_2.sce
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+

+// Theory and Problems of Thermodynamics

+// Chapter 11

+// Kinetic Theory of Gases

+// Example 2

+clear ;clc;

+

+//Given data

+P = 0.1                // pressure of helium surface exposed in MPa

+T = 300                // temperature of helium surface exposed in K

+R = 8.314              // gas constant

+M = 4*1e-3             // molecular weight of helium

+k = 1.3804*1e-23       // boltzmann constant

+

+// Calculations

+V = (8*R*T/(%pi*M))^0.5         // average velocity of gas molecule

+n = P*1e6/(k*T)                 // number of mlucules per m^3

+num_col = 1/4*n*V               // number of collisions per m^2 per second

+

+// output results

+mprintf('number of collisions per m^2 per second = %4.4f E+27', num_col*1e-27)

diff --git a/1919/CH11/EX11.3/Ex11_3.sce b/1919/CH11/EX11.3/Ex11_3.sce
new file mode 100755
index 000000000..f524a0c75
--- /dev/null
+++ b/1919/CH11/EX11.3/Ex11_3.sce
@@ -0,0 +1,32 @@
+

+// Theory and Problems of Thermodynamics

+// Chapter 11

+// Kinetic Theory of Gases

+// Example 3

+clear ;clc;

+

+//Given data

+r = 0.18                // radius of oxygen molecule in nm

+P = 0.1                 // pressure of oxygen in MPa

+T = 300                 // temperature of oxygen in K

+R = 8.314               // gas constant

+N = 6.023*1e23          // number of atoms per mole

+

+// Calculations

+v_m = R*T/(P*1e6)                     // volume occupied by one mole of gas

+V_M = N*(4/3)*%pi*((r*1e-9)^3)        // volume occupied by oxygen molecules

+

+V = v_m/N                       // volume available for one molecule

+deff('y=radius(r)', 'y = V - (4/3)*%pi*r^3') 

+r = fsolve(0.001,radius)           // radius of sphere in a molecule

+

+d = 2*r                         // average distance between 2 molecules

+

+V_E = 4*V_M                     // excluded volume for molecular motion

+

+

+// output results

+mprintf('(a) volume occupied by one mole of gas = %4.4f cubic m/mol', v_m)

+mprintf('\n (b) volume occupied by oxygen molecules = %4.4f E-05 cubic m', V_M *1e5)

+mprintf('\n (c) average distance between 2 molecules = %4.2f nm', d*1e9)

+mprintf('\n (d) excluded volume for molecular motion = %4.4f E-05 cubic m', V_E*1e5)

diff --git a/1919/CH11/EX11.4/Ex11_4.sce b/1919/CH11/EX11.4/Ex11_4.sce
new file mode 100755
index 000000000..def305250
--- /dev/null
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+

+// Theory and Problems of Thermodynamics

+// Chapter 11

+// Kinetic Theory of Gases

+// Example 4

+clear ;clc;

+

+//Given data

+T = 1000                    // Temperature of nitrogen gas in K

+M = 28*1e-3                 // molar mass of nitrogen in kg/mol

+R = 8.314                   // gas constant

+

+// Calculations

+V = (8*R*T/%pi/M)^0.5       // average speed of nitrogen

+V_rms = (3*R*T/M)^0.5       // root mean square speed of nitrogen

+V_mp = (2*R*T/M)^0.5        // most probable speed of nitrogen

+

+

+// Output results

+mprintf('Average speed of nitrogen = %4.2f m/s', V)

+mprintf('\n Root mean square speed of nitrogen = %4.2f m/s', V_rms)

+mprintf('\n Most probable speed of nitrogen = %4.2f m/s', V_mp)

diff --git a/1919/CH11/EX11.5/Ex11_5.sce b/1919/CH11/EX11.5/Ex11_5.sce
new file mode 100755
index 000000000..4bfcd337f
--- /dev/null
+++ b/1919/CH11/EX11.5/Ex11_5.sce
@@ -0,0 +1,21 @@
+

+// Theory and Problems of Thermodynamics

+// Chapter 11

+// Kinetic Theory of Gases

+// Example 5

+clear ;clc;

+

+//Given data

+V1 = 1                  // X-component velocity low range

+V2 = 1.6                // X-component velocity upper range

+

+// Caluclations

+// Required fraction from The Maxwell-Boltzmann distribution of the X-component // velocity

+

+// F = (1/sqrt(%pi))integrate(exp(-X^2),'X',1,1.6)

+// F = 1/2*((2/sqrt(%pi))integrate(exp(-X^2),'X',1,1.6) - (2/sqrt(%pi))integrate// (exp(-X^2),'X',0,1))

+

+F = 0.5*(erf(1.6) - erf(1))

+

+// Output results

+mprintf('The fraction of molecules of a gas X-component velocities in the range Vmp and 1.6Vmp = %4.4f', F)

diff --git a/1919/CH11/EX11.6/Ex11_6.sce b/1919/CH11/EX11.6/Ex11_6.sce
new file mode 100755
index 000000000..338ae2f83
--- /dev/null
+++ b/1919/CH11/EX11.6/Ex11_6.sce
@@ -0,0 +1,24 @@
+

+// Theory and Problems of Thermodynamics

+// Chapter 11

+// Kinetic Theory of Gases

+// Example 6

+clear ;clc;

+

+//Given data

+V = 1.2                // X-component velocity lower range

+

+// Caluclations

+// The fraction of molecules with positive x-component of velocity = 0.5

+F_mol = 0.5

+

+// F = (1/sqrt(%pi))integrate(exp(-X^2),'X',0,1.2)

+

+F_0 = 0.5*erf(V)

+

+// The fraction of molecules with positive X-Component of velocity greater then 1.2Vmp

+F_12 = F_mol - F_0          

+

+

+// Output results

+mprintf('The fraction of molecules with positive X-Component of velocity greater then 1.2Vmp = %4.4f', F_12)

diff --git a/1919/CH11/EX11.7/Ex11_7.sce b/1919/CH11/EX11.7/Ex11_7.sce
new file mode 100755
index 000000000..4ef0dbeff
--- /dev/null
+++ b/1919/CH11/EX11.7/Ex11_7.sce
@@ -0,0 +1,21 @@
+

+// Theory and Problems of Thermodynamics

+// Chapter 11

+// Kinetic Theory of Gases

+// Example 7

+clear ;clc;

+

+//Given data

+V1 = 1                  // X-component velocity low range

+V2 = 1.6                // X-component velocity upper range

+

+// Caluclations

+// Required fraction from The Maxwell-Boltzmann distribution of the X-component // velocity

+

+// F = (1/sqrt(%pi))integrate(exp(-X^2),'X',1,1.6)

+// F = 1/2*((2/sqrt(%pi))integrate(exp(-X^2),'X',1,1.6) - (2/sqrt(%pi))integrate// (exp(-X^2),'X',0,1))

+

+F = erf(V2) - (2/sqrt(%pi))*V2*exp(-V2^2) - erf(V1) + (2/sqrt(%pi))*exp(-V1)

+

+// Output results

+mprintf('The fraction of molecules of a gas with speed between Vmp and 1.6Vmp = %4.4f', F)

diff --git a/1919/CH11/EX11.8/Ex11_8.sce b/1919/CH11/EX11.8/Ex11_8.sce
new file mode 100755
index 000000000..2a8ec117d
--- /dev/null
+++ b/1919/CH11/EX11.8/Ex11_8.sce
@@ -0,0 +1,23 @@
+

+// Theory and Problems of Thermodynamics

+// Chapter 11

+// Kinetic Theory of Gases

+// Example 8

+clear ;clc;

+

+//Given data

+R = 8.314                       // Gas constant

+

+// u = 5*(0.5*R*T)              // Energy of molecule

+

+// h = u+Pv = 5/2*R*T + RT = 7/2*R*T     

+

+ Cv = 5/2*R

+

+ Cp = 7/2*R

+ 

+ gam = Cp/Cv

+ 

+ 

+ // output results

+ mprintf('The ratio of the molar heat capacity of CO2 = %1.1f', gam)

diff --git a/1919/CH11/EX11.9/Ex11_9.sce b/1919/CH11/EX11.9/Ex11_9.sce
new file mode 100755
index 000000000..208c3e5df
--- /dev/null
+++ b/1919/CH11/EX11.9/Ex11_9.sce
@@ -0,0 +1,30 @@
+

+// Theory and Problems of Thermodynamics

+// Chapter 11

+// Kinetic Theory of Gases

+// Example 9

+clear ;clc;

+

+//Given data

+r1 = 0.18               // radius of oxygen molecule in nm

+P = 0.01                // pressure of oxygen in MPa

+T = 500                 // temperature of oxygen in K

+R = 8.314               // gas constant

+N0 = 6.023*1e23         // number of atoms per mole

+M = 32*1e-3             // molar mass of oxygen in kg/mol

+

+// Calculations

+sig = 4*%pi*((r1*1e-9)^2)   // collision cross section

+

+n = P*N0/(R*T)              // molecules per m^3

+

+V = (8*R*T/%pi/M)^0.5       // average speed of oxygen

+

+Z = sig*n*V                 // collision frequency

+

+lam = 1/(sig*n)             // mean free path

+

+// output results

+mprintf('collision cross section for oxygen = %4.4f E-18 square m', sig*1e18)

+mprintf('\n collision frequency for oxygen = %4.0f collisions/s', Z)

+mprintf('\n mean free path for oxygen = %4.3f m', lam)