{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Chapter 4: Kinetic theory of gases" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.10: The_temperature.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear\n", "\n", "//INPUT\n", "t1=273;//temperature of the hydrogen molecule at n.t.p in K\n", "//rms value of hydrogen molecule is double to its rms value at n.t.p, so 3rt/m=4(3rt/m)\n", "\n", "//CALCULATIONS\n", "t2=4*t1;//temperature of the hydrogen molecule in K\n", "\n", "//OUTPUT\n", "mprintf('the temperature of the hydrogen molecule is %3f',t2)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.11: The_RMS_velocity.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear\n", "\n", "//INPUT\n", "t1=273;//temperature of the hydrogen molecule in K\n", "t2=373;//temperature of the hydrogen molecule in K\n", "d=0.0000896;//density of the hydrogen molecule in gm/cc\n", "p=76*13.6*981;//pressure of the hydrogen molecule in gm/cm/sec^2\n", "\n", "//CALCULATIONS\n", "v0=(3*p/d)^(0.5);//rms velocity at 0deg.C\n", "v100=v0*(t2/t1)^(0.5);//rms velocity at 100deg.C\n", "\n", "//OUTPUT\n", "mprintf('the rms velocity at 0deg.C is %3f cm/sec \n the rms velocity at 100deg.C is %3f cm/sec',v0,v100)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.12: The_RMS_velocity.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear\n", "\n", "//INPUT\n", "cp=6.84;//specific heat at constant pressure in cal/gm mole/deg.C\n", "r=8.31*10^7;//universal gas constant in ergs/gm mole/deg.C\n", "v=130000;//velocity of sound in cm/sec\n", "j=4.2*10^7;//joules constant in ergs/cal\n", "\n", "//CALCULATION\n", "cv=cp-(r/j);//specific heat at constant volume in gm-mole/deg.C\n", "y=(cp/cv);//index of co-efficient\n", "v1=(3/y)^(0.5)*v;//rms velocity in cm/sec\n", "\n", "//OUTPUT\n", "mprintf('the rms velocity of gas molecule is %3fcm/sec',v1)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.13: The_average_velocity_of_the_molecule.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear\n", "\n", "//INPUT\n", "t=300;//temperature of the oxygen molecule in K\n", "n=6.02*10^23;//avagdrao's number\n", "m=32/n;//mass of each molecule in oxygen\n", "k=1.38*10^(-16);//boltzmann constant in erg/deg\n", "\n", "//OUTPUT\n", "v=(8*k*t/(3.14*m))^(0.5);//average velocity of oxygen molecule in cm/sec\n", "v2=v*0.022384;//velocity in miles/hrs\n", "\n", "mprintf('the avg velocity of oxygen molecule is %3.1f miles/hour',v2)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.14: The_ratio_of_RMS_velocity_to_average_velocity.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear\n", "\n", "//INPUT\n", "v1=2.4;//velocity of first particle in km/sec\n", "v2=2.6;//velocity of second particle in km/sec\n", "v3=3.7;//velocity of third particle in km/sec\n", "\n", "//CALCULATIONS\n", "rv=((v1^2+v2^2+v3^2)/(3))^(0.5);//rms velocity of the particles in km/sec\n", "mv=(v1+v2+v3)/(3);//mean velocity of the particles in km/sec\n", "r=rv/mv;//ratio of the rms to mean velocity\n", "\n", "mprintf('the ratio of rms to mean velocity is %3.3f',r)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.15: The_mean_free_path.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear\n", "\n", "//INPUT\n", "n=2.76*10^19;//no.of molecules per cc\n", "d=3.36*10^(-8);//diameter of the helium molecule in cm\n", "\n", "//CALCULATIONS\n", "mf=1/((2^(0.5))*3.14*(d^2)*n)\n", "\n", "//OUTPUT\n", "mprintf('the mean free path of the hydrogen molecue is %3.8f cm',mf)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.16: The_mean_free_path_collision_rate_molecular_diameter.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear\n", "\n", "//INPUT\n", "n=85*10^(-6);//coefficent of viscosity in dynes/cm^2/velocity gradient\n", "c=16*10^4;//velocity in cm/sec\n", "p=0.000089;//density in gm/cc\n", "N=6.06*10^23/22400;//avagadro number\n", "a=(2)^(0.5)*(22/7);//constant\n", "\n", "//CALCULATIONS\n", "mf=(3*n/(p*c));//mean free path in cm\n", "cr=c/mf;//collision rate\n", "d=(1/(a*N*mf))^(0.5);//molecular diameter of hydrogen gas in cm\n", "\n", "mprintf('the mean free path is %3.6fcm \n hte collision rate is %3.2f \n the molecular diameter of hydrogen gas is %3.10fcm',mf,cr,d)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.17: The_mean_free_path.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear\n", "\n", "//INPUT\n", "d=2*10^(-8);//diameter of the molecule in cm\n", "k=1.38*10^(-6);//boltzmann constant in ergs/deg\n", "t=273;//temperature at ntp in K\n", "p=76*13.6*981;//pressure at ntp in gm/cm/sec^2\n", "\n", "//CALCULATIONS\n", "mf=((k*t)/(2^(0.5)*3.14*(d^2)*p));//mean free path in cm\n", "//since p=nkt\n", "\n", "//OUTPUT\n", "mprintf('mean free path at ntp is %3.6fcm',mf)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.18: The_diameter.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear\n", "\n", "//INPUT\n", "t=288;//temperature in K\n", "k=1.38*10^(-16);//boltzmann constant in erg/deg\n", "N=6.02*10^23;//avagadro number\n", "m=32/N;//mass of each oxygen molecule in gm\n", "v=196*10^-6;//viscosity in poise\n", "\n", "//CALCULATIONS\n", "av=((8*k*t/(3.14*m))^0.5);//average velocity in cm/sec\n", "d=(m*av/(3*3.14*2^(0.5)*v))^0.5;//diameter of the molecule in cm\n", "\n", "mprintf('diameter of the molecule is %3.10f cm',d)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.19: The_pressure.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear\n", "\n", "//INPUT\n", "mf=15;//mean free path in cm\n", "t=300;//temperature of oxygen molecule in K\n", "d=3*10^(-8);//diameter of the molecule in cm\n", "N=6.02*10^23;//avagadro number\n", "r=8.32*10^7;//universal gas constant in ergs/mole/deg\n", "a=(2^(0.5))*(22/7);\n", "\n", "//CSLCULATIONS\n", "p=(r*t)/(N*a*(d^2)*mf);//pressure of the oxygen molecule in dynes/sq.cm\n", "\n", "//OUTPUT\n", "mprintf('the pressure of the oxygen molecule is %3.3f dynes/sq.cm',p)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.1: The_temperature.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear\n", "\n", "//INPUT\n", "t=273;//temperture of the oxygen molecule in K\n", "m=32;//molecular mass of the gas in gm\n", "r=8.32*10^7;//molar gas constant in ergs per mole\n", "v2=33200;//velocity of the gas in cm/sec\n", "\n", "//CALCULATIONS\n", "v1=((3*r*t)/m)^(1/2);//rms velocity of the molecule in cm/s\n", "T=((v2*v2*m)/(3*r));//temperature of the molecule with sound has velocity in K\n", "\n", "//OUTPUT\n", "mprintf('the rms velocity of the molecule is %3.2fcm/s \n the temperature of the molecule is %3.0fK',v1,T)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.20: The_avagadro_number.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear\n", "\n", "//INPUT\n", "k=5.64*10^-14;//kinetic energy of the hydrogen molecule ergs\n", "t=273;//temperature of the oxygen molecule in K\n", "r=8.32*10^7;//universal gas constant in ergs \n", "\n", "//CALCULATIONS\n", "N=(3/2)*(r*t/k);//avagadro number\n", "\n", "//OUTPUT\n", "mprintf('the avagadro number is %3.2f',N)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.21: The_number_which_will_be_travelling_undeflected.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear\n", "\n", "//INPUT\n", "q=5000;//total number of molecules\n", "e=2.7183;//constant value\n", "t1=0.5;//distance travled to the mean free path\n", "t2=1;//distance travelled to the mean free path\n", "\n", "//CALCULATONS\n", "p1=q*(e^-t1);//n0.of molecules having no collision in traversing a distance t1\n", "p2=q*(e^-t2);//n0.of molecules having no collision in traversing a distance t2\n", "\n", "//OUPUT\n", "mprintf('the no. of molecules having no collision in traversing a distance o.5 is %3f \n the no. of molecules having no collision in traversing a distance 1 is %3f',p1,p2)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.22: The_mean_kinetic_energy.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear\n", "\n", "//INPUT\n", "t=38380;//temperature of the molecule in K\n", "k=1.38*10^-16;//boltzman constant of one electron in ergs/K\n", "e=1.6*10^-12;//charge of one electron volts\n", "\n", "//CALCULATIOS\n", "mk=1.5*k*t/e;//mean kinetic energy per atom in ev\n", "\n", "//OUTPUT\n", "mprintf('the mean kinetic energy of the molecule is %3.3f ev',mk) " ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.23: The_mean_free_path_and_the_collision_frequency.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear\n", "\n", "//INPUT\n", "v=1.7*10^-4;//viscosity of the air molecule in cgs\n", "d=0.00129;//density of the molecule in gm/ml\n", "p=76*13.6*981;//pressure of the molecule in gm/cm/sec^2\n", "\n", "//CALCULATIONS\n", "r=(3*p/d)^(0.5);//rms velocity of the molecule in cm/sec\n", "mf=(3*v/(d*r));//mean free path in cm\n", "cf=r/mf;//collision frequency\n", "\n", "//OUTPUT\n", "mprintf('the mean free path is %3.7f cm \n the collision frequency is %3f',mf,cf)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.24: The_pressure_of_the_gas.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear\n", "\n", "//INPUT\n", "t2=296.4;//temperature of the first plate in K\n", "t1=304.7;//temperature of the second plate in K\n", "f=1.6*10^-2;//force repelled cold is dynes/sq.cm\n", "\n", "//CALCULATIONS\n", "p=(4*f*t2/(t1-t2));//pressure of the gas in dynes/sq.cm\n", "\n", "//OUTPUT\n", "mprintf('the pressure of the gas is %3.3f dynes/sq.cm',p)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.25: The_size_of_helium_atom.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear\n", "\n", "//INPUT\n", "mf=28.5*10^-6;//mean free path in cm\n", "d=0.000178;//density of helium in gm/ml\n", "m=6*10^-24;//mass of the helium atom in gm\n", "a=(2^(0.5))*3.14;//constant\n", "\n", "//CALCULATIONS\n", "d=(m/(a*d*mf))^(0.5);//diameter of the size in cm\n", "\n", "//OUTPUT\n", "mprintf('the size of the helium atom is %3.10f cm',d)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.26: The_value_avagadro_number.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear\n", "\n", "//INPUT\n", "a1=0*10^-4;//first horizontal displacement in cm\n", "a2=5.6*10^-4;//second horizontal displacement in cm\n", "a3=-4.7*10^-4;//third horzontal displacement in cm\n", "a4=-10.8*10^-4;//fourth horizontal displacement in cm\n", "a5=6.6*10^-4;//fifth horizontal displacement displacement in cm\n", "a6=-9.8*10^-4;//sixth horizontal displacement in cm\n", "a7=-11.2*10^-4;//7th horizontal displacement in cm\n", "a8=-4.0*10^-4;//8th horizontal displacement in cm\n", "a9=15.0*10^-4;//9thhorizontal displacement in cm\n", "a10=19.1*10^-4;//10th horizontal displacement in cm\n", "a11=16.0*10^-4;//11ht horizontal displacement in cm\n", "T=293;//temperature of the particle in K\n", "v=0.01;//viscosity in cgs\n", "r=1.15*10^-5;//radius of the particle in cm\n", "R=8.32*10^7;//universal gas constant in kj/kg mole\n", "t=30;//time for observation of each in sec\n", "\n", "//CALCULATIONS\n", "x=(a1^2+a2^2+a3^2+a4^2+a5^2+a6^2+a7^2+a8^2+a9^2+a10^2+a11^2)/11\n", "n=R*T*t/(x*3*3.14*v*r);//no.of molecules in the observation \n", "\n", "//OUTPUT\n", "mprintf('the value of n is %3f',n)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.27: The_fractional_change_in_the_number_of_helium_atoms.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear\n", "\n", "//INPUT\n", "m=6*10^-24;//mass of the helium atom in gm\n", "k= 1.38*10^-16;//boltzmann constant in erg\n", "t1=100;//temperature in K\n", "t2=900;//temperature in K\n", "\n", "//CALCULATIONS\n", "r=(t1/t2)^(3/2)*(2.7183^(m*(1/(2*k))*10^8*(1-(1/9))));//fractional change in the no.of helium atoms\n", "\n", "//OUPUT\n", "mprintf('the fractional change in the no.of helium atoms %3.4f',r)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.2: The_temperature.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear\n", "\n", "//INPUT\n", "t1=308;//temperature of the nitrogen molecule in K\n", "m1=28;//molecular mass of the nitrogen in gm\n", "m2=2;//molecular mass of the hydrogen molecule in gm\n", "\n", "//CALCULATIONS\n", "t2=(t1*m2/m1);//temperature of the hydrogen molecule in K\n", "//GIVEN avg.speed of both the molecules are same\n", "\n", "//OUTPUT\n", "mprintf('the temperature of the hydrogen molecule is %3.0fK',t2)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.3: The_RMS_velocity_at_NTP.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear\n", "\n", "//INPUT\n", "y=0.00129;//density of the air in gm/cc\n", "p=76;//pressure of the nitrogen molecule in cm\n", "g=981;//accelaration due to gravity in cm/sec^2\n", "m=13.6;//density of the mercury in gm/cc\n", "\n", "//CALCULATIONS\n", "v=((3*p*g*m)/y)^(1/2);//rms velocity of air at ntp in cm/sec\n", "\n", "//OUTPUT\n", "mprintf('the rms velocity of the air is %3.2fcm/sec',v)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.4: The_rms_velocity.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear\n", "\n", "//INPUT\n", "d=16*0.000089;//density of the oxygen molecule in gm/cc\n", "p=76;//pressure of the air in cm\n", "g=981;//gravitaitonal accelaration in cm/sec^2\n", "m=13.6;//density of the mercury in gm/cc\n", "\n", "//CALCULATIONS\n", "v=((3*p*g*m)/d)^(1/2);//velocuty of the oxygen molecule in cm/sec\n", "\n", "//OUTPUT\n", "mprintf('velocity of oxygen molecule is %3.2fcm/sec',v)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.5: The_kinetic_energy_of_hydrogen_molecule.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear\n", "\n", "//INPUT\n", "t=273;//temperature of the hydrogen molecule in K\n", "n=6.03*10^23;//1 mole of hydrogen molecules\n", "r=8.31*10^7;//universal gas constant in erg/K/mole\n", "\n", "//CALCULATIONS\n", "e=(1.5*r*t)/n;//kinetic energy of the hydrogen molecule in erg\n", "\n", "//OUTPUT\n", "mprintf('the kinetic energy of the hydrogen molecule is %3.16ferg',e)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.6: The_kinetic_energy.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear\n", "\n", "//INPUT\n", "m=1;//mass of the oxygen in gm\n", "r=8.31*10^7;//universal gas constant in erg/K/mole\n", "t=320;//temperature of the oxygen in K\n", "//for 1gm mole k.e is 1.5rt then for 1 gm oxygen (1/32)(k.e)\n", "\n", "//CALCULATIONS\n", "e=(m/32)*(3*r*t/2);//kinetic energy of the oxygen in erg\n", "\n", "//OUTPUT\n", "mprintf('the kinetic energy of the oxygen is %3.2ferg',e)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.7: The_temperature.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear\n", "\n", "//INPUT\n", "t=273;//temperature at ntp in K\n", "//rms velocity of oxygen is 3/2 times its rms velocity at ntp then e1=(3/2)*e\n", "\n", "//CALCULATIONS\n", "t1=(9*t/4);//temperature of the oxygen molecule in K\n", "\n", "//OUTPUT\n", "mprintf('temperature of the oxygen in %3.2fK',t1)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.8: The_kinetic_energy.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear\n", "\n", "//INPUT\n", "p=10;//pressure of the gas in atm\n", "v=5000;//volume of the gas in ml\n", "l=76;//length of the mercury in barometer in cm\n", "g=981;//accelaration due to gravity in cm/sec^2\n", "d=13.6;//density of the mercury in gm/cc\n", "\n", "//CALCULATIONS\n", "e=3*p*v*l*g*d;//kinetic energy of the molecule in ergs\n", "\n", "//OUTPUT\n", "mprintf('the kinetic energy of the molecule is %3.2fergs',e)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.9: The_molecular_energy.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear\n", "\n", "//INPUT\n", "t=323;//temperature of the hydrogen molecule in K\n", "m1=1;//mass of the hydrogen molecule in gm\n", "m2=2;//molecular weight of the hydrogen in gm\n", "r=8.3*10^7;//universal gas constant in erg/K/mole\n", "\n", "//CALCULATIONS\n", "e=(m1*r*t*3/(m2*2));//kinetic enrgy of the hydrogen molecule in ergs\n", "\n", "//OUTPUT\n", "mprintf('the kinetic energy of the molecule is %3.2fergs',e)" ] } ], "metadata": { "kernelspec": { "display_name": "Scilab", "language": "scilab", "name": "scilab" }, "language_info": { "file_extension": ".sce", "help_links": [ { "text": "MetaKernel Magics", "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" } ], "mimetype": "text/x-octave", "name": "scilab", "version": "0.7.1" } }, "nbformat": 4, "nbformat_minor": 0 }