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   "source": [
    "# Chapter 3 : Zeroth Law of Thermodynamics and Temperature Scales"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 3.1 Page No : 72"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "When the temperature is 303 K then the thermometer reading in °F is : 86\n",
      "The absolute value of the temperature in Rankine scale in °R is : 546\n"
     ]
    }
   ],
   "source": [
    "\n",
    "# Variables\t\t\t\n",
    "t_c = 303-273;\t\t\t# in °C\n",
    "\n",
    "# Calculations and Results\n",
    "t_f = 9./5* t_c+32;\t\t\t# in °F\n",
    "print \"When the temperature is 303 K then the thermometer reading in °F is : %.0f\"%t_f\n",
    "\n",
    "T_R = 460 + t_f;\t\t\t# °R\n",
    "print \"The absolute value of the temperature in Rankine scale in °R is : %.0f\"%T_R\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 3.2 Page No : 73"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Temperature in kelvin is : 274.29\n",
      "Temperature in °R is : 460.81\n",
      "Temperature in °C is : 1.14\n",
      "Temperature in °F is : 1.14\n"
     ]
    }
   ],
   "source": [
    "\n",
    "\n",
    "# Variables\n",
    "# t_C= t_F or T_K-T_R= -186.52     (i)\n",
    "# T_R/T_K = 1.68                                (ii)\n",
    "# From eq (i) and (ii)\n",
    "T_K= -186.52/(1-1.68);\t\t\t# temp. in kelvin in K\n",
    "\n",
    "# Calculations\n",
    "T_R= 1.68*T_K;\t\t\t    # in temp. in rankine in °R\n",
    "t_C= T_K-273.15;\t\t\t# in °C\n",
    "t_F= T_R-459.67;\t\t\t# in °F\n",
    "\n",
    "# Results\n",
    "print \"Temperature in kelvin is : %.2f\"%T_K\n",
    "print \"Temperature in °R is : %.2f\"%T_R\n",
    "print \"Temperature in °C is : %.2f\"%t_C\n",
    "print \"Temperature in °F is : %.2f\"%t_F\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 3.9 Page No : 75"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The temperature at p=2.5 in °unit is : 73.014\n"
     ]
    }
   ],
   "source": [
    "import math \n",
    "\n",
    "# Variables\n",
    "p0 = 1.86;\n",
    "p100 = 6.81;\n",
    "T1=32;\n",
    "T2= 212;\n",
    "\n",
    "# Calculations\n",
    "# Relation of T in terms of p for ice point      T1= a*math.log(p0)+b          (i)\n",
    "# Relation of T in terms of p for steam point  T2= a*math.log(p100)+b     (ii)\n",
    "# From eq(i) and (ii)\n",
    "a= (T2-T1)/math.log(p100/p0);\n",
    "b= T1-a*math.log(p0);\n",
    "# The temp at \n",
    "p=2.5;\n",
    "T= a*math.log(p)+b;\t\t\t# in °unit\n",
    "\n",
    "# Results\n",
    "print \"The temperature at p=2.5 in °unit is : %.3f\"%T\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 3.10 Page No : 76"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "When P reads 20°C, then the readings of  Q in °C are 18.76 C \n",
      "The realistic value of Tq in °C is : 18.76\n"
     ]
    }
   ],
   "source": [
    "\n",
    "from numpy import roots\n",
    "\n",
    "# Variables\t\t\t\n",
    "Tp0=0.;\t\t\t#in °C (at ice point)\n",
    "Tq0=0.;\t\t\t#in °C (at ice point)\n",
    "                # Putting these values in relation, we get\n",
    "a=0.;\n",
    "Tp100=100.;\t\t\t#in °C ( at steam point)\n",
    "Tq100=100.;\t\t\t#in °C ( at steam point)\n",
    "                # Tp100= b*Tq100+lamda*Tq100**2         (i)\n",
    "Tp=45.;\t\t\t# in °C (in oil path)\n",
    "Tq=43.;\t\t\t# in °C (in oil path)\n",
    "\n",
    "# Calculations\n",
    "# Tp= b*Tq+lamda*Tq**2                          (ii)\n",
    "b= (Tp100-Tp*Tq100**2/Tq**2)/(Tq100-Tq100**2/Tq);\t\t\t# From eq (i) and (ii)\n",
    "lamda= (Tp-b*Tq)/Tq**2;\n",
    "Tp=20;\n",
    "\n",
    "#lamda*Tq**2+b*Tq-Tp=0\n",
    "P= [lamda, b, -Tp];\n",
    "Tq= roots(P);\t\t\t# in °C\n",
    "\n",
    "# Results\n",
    "print \"When P reads 20°C, then the readings of  Q in °C are %.2f C \"%(Tq[1])\n",
    "print \"The realistic value of Tq in °C is : %.2f\"%Tq[1]\n"
   ]
  }
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