path: root/Heat_And_Thermodynamics_by_A_Manna/8-First_law_of_thermodynamics.ipynb

{
"cells": [
 {
		   "cell_type": "markdown",
	   "metadata": {},
	   "source": [
       "# Chapter 8: First law of thermodynamics"
	   ]
	},
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.10: The_final_temperature_and_pressure.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"\n",
"//INPUT\n",
"p1=76;//inital pressure in cm\n",
"t1=290;//inital temperature in K\n",
"y=1.4;//coefficent of expansion\n",
"dv=2;//ratio of inital to fianl volume when air expands isothermally \n",
"dv1=2;//ratio of inital to final volume when air expands adiabatically\n",
"\n",
"//CALCULATIONS\n",
"p2=p1/dv;//final pressure when air expands isothermally in cm of hg\n",
"t2=t1;//final temperature when air expands isothermally in K\n",
"t3=t2*(1/dv1)^(y-1);//temprature when air expands adiabatically in K\n",
"p3=p2*(1/dv1)^(y);//final pressure when air expands adiabatically in mm of hg\n",
"\n",
"//OUTPUT\n",
"mprintf('final pressure when air expands isothermally in cm of hg %3.2f mm of hg \n final temperature when air expands isothermally is %3.2f K \n temprature when air expands adiabatically is %3.2f K \n final pressure when air expands adiabatically is %3.2f mm of hg',p2,t2,t3,p3)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.11: The_work_done.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"\n",
"//INPUT\n",
"p=76*13.6*981;//pressure of air in dynes/sq.cm\n",
"v=11100;//volume expanded in ml\n",
"t1=273;//inital temperature in K\n",
"t2=274;//final temperature in K\n",
"cv=2.411;//specific heat at constant volume in cal/K\n",
"j=4.2*10^7;//joules constant in ergs/cal\n",
"//CALCULATIONS\n",
"w=p*v*log(t2/t1);//work done in ergs\n",
"h=cv*(t2-t1)+w/j;//heat supplied in cal\n",
"\n",
"//OUTPUT\n",
"mprintf('the work done is %3.2f erg \n the heat supplied is %3.3f cal',w,h)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.12: The_work_done.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"\n",
"//INPUT\n",
"p=10^6;//pressure of air in dynes\n",
"d=0.0001293;//density of air in gm/cc\n",
"t1=273;//inital temperature in K\n",
"dv=2;//ratio of inital volume to final volume\n",
"y=1.4;//coefficient of expansion\n",
"\n",
"//CALCULATIONS\n",
"r=p/(d*t1);//universal gas constant in dynes.cc/gm.K\n",
"t2=t1*(dv)^(y-1);//final temperature in K\n",
"w=r*(t2-t1)/(y-1);//work done in adiabatic compression in ergs\n",
"\n",
"//OUTPUT\n",
"mprintf('work done in adiabatic compression is %3.2f ergs',w)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.13: The_change_in_internal_energy.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"\n",
"//INPUT\n",
"m=5;//mass of air in gm\n",
"cv=0.172;//specific heat at constant volume cal/gm\n",
"dt=10;//changi in temperature in K\n",
"\n",
"//CALCULATIONS\n",
"ie=m*cv*dt;//change in internal energy in cal\n",
"\n",
"//OUTPUT\n",
"mprintf('change in internal energy is %3.2f cal',ie)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.14: The_heat_supplied.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"\n",
"//INPUT\n",
"v1=10^3;//inital volume in cc\n",
"v2=2*v1;//final volume in cc\n",
"p1=76*13.6*981;//pressure in dyne/sq.cm\n",
"t1=273;//intial temperature in K\n",
"d=1.29;//density of the gas gm/lit\n",
"cv=0.168;//specific heat at constant volume in cal/gm\n",
"\n",
"//CALCULATIONS\n",
"t2=(v2/v1)*t1;//final temperature in K\n",
"r=0.068;//universal gas constant in cal\n",
"cp=cv+r;//specific heat at constant pressure in cal\n",
"q=d*cp*(t2-t1);//heat supplied in cal\n",
"\n",
"//OUTPUT\n",
"mprintf('the heat supplied to the gas is %3.2f cal',q)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.15: The_maximum_work_done.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"\n",
"//INPUT\n",
"t=303;//temperature of the one mole of the argon in K\n",
"v1=1;//intial volume in litres\n",
"v2=10;//final volume in litres\n",
"r=8.31*10^7;//universal gas constant in ergs/K.mol\n",
"\n",
"//CALCULATIONS\n",
"w=r*t*log(v2/v1);//work done in isothermal expansion in ergs\n",
"\n",
"//OUTPUT\n",
"mprintf('the work done in isothermal expansion is %3.2f ergs',w)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.16: The_amount_of_heat_absorbed.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"\n",
"//INPUT\n",
"dv=4;//final volume of neon in lit\n",
"t=273;//temperature of the gas in K\n",
"n=2.6/22.4;//the no.of moles of neon\n",
"r=1.98;//universal gas constant in cal/K.mol\n",
"\n",
"//CALCULATIONS\n",
"w=n*t*r*log(dv);//work done by gas in ergs\n",
"\n",
"//OUTPUT\n",
"mprintf('the work done by 2.6lit of neon is %3.2f ergs',w)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.18: The_temperature.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"\n",
"//INPUT\n",
"dv=10^(-3);//ratio of initial and final volume\n",
"t1=10^5;//initial temperature in K\n",
"y=1.66;//coefficient of expansion\n",
"\n",
"//CALCULATIONS\n",
"t2=t1*(dv)^(y-1);//final temperature in K\n",
"\n",
"//OUTPUT\n",
"mprintf('final temperature of the gas is %3.2f K',t2)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.19: The_value_coefficient_of_expansion.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"\n",
"//INPUT\n",
"p1=8;//intial pressure in cm of hg\n",
"p2=6;//final pressure in cm of hg\n",
"v1=1000;//intial volume in cc\n",
"v2=1190;//final volume in cc\n",
"\n",
"//CALCULATIONS\n",
"y=log(p1/p2)/log(v2/v1);//coefficient of expansion\n",
"\n",
"//OUTPUT\n",
"mprintf('the coefficent of expansion is %3.2f',y)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.1: The_change_in_internal_energy.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"\n",
"//INPUT\n",
"l=80;//latent heat of fusion in cal\n",
"j=4.2*10^7;//joules constant in ergs/cal\n",
"w=-0.092*10^6;//work done in changing phase change in ergs\n",
"\n",
"//CALCULATIONS\n",
"q=l*j;//heat added in ergs\n",
"du=q-w;//internal energy in ergs\n",
"\n",
"//OUTPUT\n",
"mprintf('the change in internal energy is %3.2f ergs',du)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.2: The_change_in_internal_energy.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"\n",
"//INPUT\n",
"m=1;//mass in gm\n",
"l=536;//latent heat in cal/gm\n",
"j=4.2*10^7;//joules constant in ergs/cal\n",
"v=1649;//volume of water in cc\n",
"p=76*13.6*981;//pressure of water in dynes/sq.cm\n",
"\n",
"//CALCULATIONS\n",
"dq=m*l*j;//heat supplied in ergs\n",
"dw=p*v;//work done in ergs\n",
"du=dq-dw;//internal energy developed in ergs\n",
"\n",
"//OUTPUT\n",
"mprintf('internal energy of water is %3.2f ergs',du)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.3: The_temperature_immediately_after_the_compressio.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"\n",
"//INPUT\n",
"dv=10;//ratio of original volume to final volume\n",
"t1=293;//inital temperature in K\n",
"y=1.41;//coefficent of expansion\n",
"\n",
"//CALCULATIONS\n",
"t2=t1*(dv)^(y-1);//final temperature in K\n",
"\n",
"//OUTPUT\n",
"mprintf('the final temperature is %3.2f K',t2)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.4: The_change_in_temperature.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"\n",
"//INPUT\n",
"t=273;//temperature of earth at height h in K\n",
"p=760;//pressure in mm of hg\n",
"dp=1;//change in pressure in mm of hg\n",
"y=1.418;//coefficient of expansion\n",
"\n",
"//CALCULATIONS\n",
"dt=((y-1)/y)*dp*t/p;//change in temperature in deg.C\n",
"\n",
"//OUTPUT\n",
"mprintf('the change in temperature is %3.3f deg.C',dt)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.5: The_resulting_drop_in_temperature.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"\n",
"//INPUT\n",
"p1=2;//pressure initial in atm\n",
"p2=1;//pressure final in atm\n",
"t1=288;//inital temperature in K\n",
"y=1.4;//coefficent of expansion\n",
"\n",
"//CALCULATIONS\n",
"t2=t1*(p2/p1)^((y-1)/y);//final temperature in K\n",
"dt=t1-t2;//drop in temperature in K\n",
"\n",
"//OUTPUT\n",
"mprintf('drop in temperature is %3.2f K',dt)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.6: The_resultant_temperature.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"\n",
"//INPUT\n",
"t1=288;//inital temperature in K\n",
"dv=1/2;//ratio of inital to final volume\n",
"y=1.4;//coefficient of expansion\n",
"\n",
"//CALCULATIONS\n",
"t2=t1*(dv)^(y-1);//final temperature in K\n",
"\n",
"//OUTPUT\n",
"mprintf('the final temperature is %3.1f K',t2)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.7: The_resultant_rise_in_temperatures_in_both_the_cases.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"\n",
"//INPUT\n",
"y=1.4;//coefficent of exapnsion\n",
"p1=1;//standard pressure in atm\n",
"dv=50;//ratio of initial volume to final volume\n",
"t1=273;//standard temperature in K\n",
"\n",
"//CALCULATIONS\n",
"p2=p1*dv;//final pressure when slowly compressed in atm\n",
"p3=p1*(dv)^(y);//final pressure when suddenly compressed in atm\n",
"t2=t1*(dv)^(y-1);//rise in temperature when it is suddenly compressed in K\n",
"\n",
"//OUTPUT\n",
"mprintf('the final pressure when it is compressed slowly is %3fatm \n the final pressure when it is compressed suddenly is %3.2fatm \n the rise in temperature when it is suddenly compressed is %3.0fK',p2,p3,t2)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.8: The_rise_in_temperature.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"\n",
"//INPUT\n",
"y=1.5;//coefficient of expansion\n",
"dp=1/8;//ratio of inital pressure to final pressure\n",
"t1=300;//inital tempreature in K\n",
"\n",
"//CALCULATIONS\n",
"t2=t1*(dp)^((1-y)/y);//change in temperature in K\n",
"t3=t2-t1;//rise in temperature in K\n",
"\n",
"//OUTPUT\n",
"mprintf('the rise in temperature is %3.2f K',t3)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.9: The_amount_of_work_done.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"\n",
"//INPUT\n",
"t1=400;//inital temperature in K\n",
"dv=2;//ratio of volumes final and inital\n",
"r=8.31*10^7;//universal gas constant in ergs/kg.K\n",
"\n",
"//CALCULATIONS\n",
"w=r*t1*log(2);//work done in expanding isothermally in ergs\n",
"\n",
"//OUTPUT\n",
"mprintf('the work done in expanding isothermally is %3.2f ergs',w)"
   ]
   }
],
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