{ "metadata": { "name": "", "signature": "sha256:981d9d414fb3ccab1f09efa00cc14135798c564e57ce294278994d4eafe77df4" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 3 : Calorimetry\n" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.1 Page No : 49" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "# Input data\n", "T = 5. # Time taken for a liquid to cool from 80 to 50 degree centigrade in minutes\n", "t11 = 80. # The initial temperature of the liquid in degree centigrade\n", "t12 = 50. # The final temperature of the liquid in degree centigrade\n", "t21 = 60. # If the initial temperature of the liquid in degree centigrade\n", "t22 = 30. # If the final temperature of the liquid in degree centigrade\n", "ts = 20. # The temperature of the surrounding in degree centigrade\n", "\n", "# Calculations\n", "# The time taken for the liquid to cool from 60 to 30 degree centigrade in\n", "# minutes\n", "T1 = ((math.log((t22 - ts) / (t21 - ts))) /\n", " (math.log((t12 - ts) / (t11 - ts)))) * T\n", "\n", "# Output\n", "print 'The time taken for a liquid to cool from 60 to 30 degree centigrade is t = %3.0f minutes ' % (T1)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The time taken for a liquid to cool from 60 to 30 degree centigrade is t = 10 minutes \n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.2 Page No : 55" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Input data\n", "dw = 1. # The density of water in g/cm**3\n", "da = 0.8 # The density of alcohol in g/cm**3\n", "t1 = 100. # The time taken for the water to cool from 50 to 40 degree centigrade in seconds\n", "t2 = 74. # The time taken for the alcohol to cool from 50 to 40 degree centigrade in seconds\n", "V = 1. # Let the volume of either liquid be in cm**3\n", "\n", "# Calculations\n", "m = V * dw # The mass of water in g\n", "M = V * da # The mass of alcohol in g\n", "w = V # Water equivalent of each calorimeter in cm**3\n", "# The specific heat of alcohol in calorie/g-K\n", "C = ((((m + w) * t2) / (M * t1)) - (w / M))\n", "\n", "# Output\n", "print 'The specific heat of alcohol is C = %3.1f calorie/g-K' % (C)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The specific heat of alcohol is C = 0.6 calorie/g-K\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.3 Page No : 61" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "# Input data\n", "t = 5. # Time taken for a body to cool from 60 to 40 degree centigrade in minutes\n", "t11 = 60. # The initial temperature of the body in degree centigrade\n", "t12 = 40. # The final temperature of the body in degree centigrade\n", "ts = 10. # The temperature of the surrounding in degree centigrade\n", "\n", "# Calculations\n", "# The constant value for the first case at ts\n", "K = math.log((t12 - ts) / (t11 - ts))\n", "# The temperature after the next 5 minutes in degree centigrade\n", "x = ((math.exp(K)) * (t12 - ts)) + ts\n", "\n", "# Output\n", "print 'The temperature after the next 5 minutes is x = %3.0f degree centigrade ' % (x)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The temperature after the next 5 minutes is x = 28 degree centigrade \n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.4 Page No : 63" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "# Input data\n", "T = 4. # Time taken for a liquid to cool from 70 to 50 degree centigrade in minutes\n", "t11 = 70. # The initial temperature of the liquid in degree centigrade\n", "t12 = 50. # The final temperature of the liquid in degree centigrade\n", "t21 = 50. # If the initial temperature of the liquid in degree centigrade\n", "t22 = 40. # If the final temperature of the liquid in degree centigrade\n", "ts = 25. # The temperature of the surrounding in degree centigrade\n", "\n", "# Calculations\n", "# The time taken for the liquid to cool from 50 to 40 degree centigrade in\n", "# minutes\n", "T1 = ((math.log((t22 - ts) / (t21 - ts))) /\n", " (math.log((t12 - ts) / (t11 - ts)))) * T\n", "\n", "# Output\n", "print 'The time taken for a liquid to cool from 50 to 40 degree centigrade is t = %3.3f minutes ' % (T1)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The time taken for a liquid to cool from 50 to 40 degree centigrade is t = 3.476 minutes \n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.5 Page No : 67" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "# Input data\n", "t = 6. # Time taken for a liquid to cool from 80 to 60 degree centigrade in minutes\n", "T = 10. # To find the temperature after the time in minutes\n", "t11 = 80. # The initial temperature of the liquid in degree centigrade\n", "t12 = 60. # The final temperature of the liquid in degree centigrade\n", "ts = 30. # The temperature of the surrounding in degree centigrade\n", "\n", "# Calculations\n", "# The constant value for the first case at ts\n", "K = (math.log((t12 - ts) / (t11 - ts))) / (-t)\n", "# The temperature after the next 10 minutes in degree centigrade\n", "x = ((math.exp(-T * K)) * (t12 - ts)) + ts\n", "\n", "# Output\n", "print 'The temperature after the next 10 minutes is x = %3.2f degree centigrade ' % (x)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The temperature after the next 10 minutes is x = 42.80 degree centigrade \n" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.6 Page No : 69" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "# Input data\n", "t = 5. # The time taken for a body to cool from 80 to 64 degree centigrade in minutes\n", "t11 = 80. # The initial temperature of the body in degree centigrade\n", "t12 = 64. # The final temperature of the body in degree centigrade\n", "t21 = 52. # The temperature of the body after 10 minutes in degree centigrade\n", "T = 10. # The time taken for a body to cool from 80 to 52 degree centigrade in minutes\n", "T1 = 15. # To find the temperature after the time in minutes\n", "\n", "# Calculations\n", "# The temperature of the surroundings in degree centigrade\n", "ts = ((t21 * t11) - (t12**2)) / (t11 + t21 - (2 * t12))\n", "# The constant value for the first case at ts\n", "K = (math.log((t21 - ts) / (t12 - ts)))\n", "# The temperature after the next 15 minutes in degree centigrade\n", "x = ((math.exp(K)) * (t21 - ts)) + ts\n", "\n", "# Output\n", "print '(1)The temperature of the surroundings is %3.0f degree centigrade \\n (2)The temperature after the 15 minutes is %3.0f degree centigrade ' % (ts, x)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(1)The temperature of the surroundings is 16 degree centigrade \n", " (2)The temperature after the 15 minutes is 43 degree centigrade \n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.7 Page No : 76" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Input data\n", "t2 = 2. # The time taken for the liquid to cool from 50 to 40 degree centigrade in minutes\n", "t11 = 50. # The initial temperature of the liquid in degree centigrade\n", "t12 = 40. # The final temperature of the liquid in degree centigrade\n", "t1 = 5. # The time taken for the water to cool from 50 to 40 degree centigrade in minutes\n", "m = 100. # The mass of water in gms\n", "M = 85. # The mass of liquid in gms\n", "w = 10. # Water equivalent of the vessel in gms\n", "\n", "# Calculations\n", "# The specific heat of a liquid in calories/g-K\n", "C = (((m + w) * (t2 * 60)) / (M * (t1 * 60))) - (w / M)\n", "\n", "# Output\n", "print 'The specific heat of a liquid is C = %3.1f calories/g-K' % (C)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The specific heat of a liquid is C = 0.4 calories/g-K\n" ] } ], "prompt_number": 7 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.8 Page No : 79" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Input data\n", "V = 22400. # The volume of One gram molecule of a gas at N.T.P in cm**3\n", "p = 76. # The pressure in cm of Hg\n", "T = 273. # The temperature in K\n", "\n", "# Calculations\n", "P = p * 13.6 * 981 # The pressure in dynes/cm**2\n", "# The universal gas constant for one gram molecule of a gas in ergs/mole-K\n", "R = (P * V) / T\n", "\n", "# Output\n", "print 'The universal gas constant for one gram molecule of a gas is R = %3.4g ergs/mole-K' % (R)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The universal gas constant for one gram molecule of a gas is R = 8.32e+07 ergs/mole-K\n" ] } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.9 Page No : 83" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Input data\n", "Cp = 0.23 # Specific heat of air at constant pressure\n", "J = 4.2 * 10**7 # The amount of energy in ergs/cal\n", "d = 1.293 # The density of air at N.T.P in g/litre\n", "p = 76. # The pressure in cm of Hg\n", "T = 273. # The temperature in K\n", "\n", "# Calculations\n", "P = p * 13.6 * 980 # The pressure in dynes/cm**2\n", "V = (1000 / d) # Volume of one gram of air at N.T.P in cm**3\n", "r = (P * V) / T # The gas constant for one gram of a gas in ergs/g-K\n", "Cv = Cp - (r / J) # Specific heat of air at constant volume\n", "\n", "# Output\n", "print 'The specific heat of air at constant volume is Cv = %3.4f ' % (Cv)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The specific heat of air at constant volume is Cv = 0.1617 \n" ] } ], "prompt_number": 9 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.10 Page No : 88" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Input data\n", "w = 4. # The Molecular weight of helium\n", "v = 22400. # The volume of one gram molecule of a gas at N.T.P in cm**3\n", "p = 76. # The pressure in cm of Hg\n", "T = 273. # The temperature in K\n", "J = 4.2 * 10**7 # The amount of energy in ergs/cal\n", "\n", "# Calculations\n", "V = (v / w) # The volume of one gram of helium at N.T.P in cm**3\n", "P = p * 13.6 * 980 # The pressure in dynes/cm**2\n", "r = (P * V) / T # The gas constant for one gram of a gas in ergs/g-K\n", "C = r / J # The difference in the two specific heats of one gram of helium\n", "\n", "# Output\n", "print 'The difference in the two specific heats of one gram of helium is Cp-Cv = %3.4f' % (C)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The difference in the two specific heats of one gram of helium is Cp-Cv = 0.4947\n" ] } ], "prompt_number": 10 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.11 Page No : 94" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Input data\n", "V = 25. # Volume of gasoline consumed by an engine in litres/hour\n", "cv = 6. * 10**6 # The calorific value of gasoline in calories/litre\n", "P = 35. # The output of the engine in kilowatts\n", "\n", "# Calculations\n", "h = V * cv # Total heat produced by gasoline in one hour in calories\n", "H = h / 3600 # Heat produced per second in cal/s\n", "I = H * 4.2 # Heat produced per second in joules/s or watts\n", "E = ((P * 1000) / I) * 100 # The efficiency in percent\n", "\n", "# Output\n", "print 'The efficiency of the engine is %3.0f percent ' % (E)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The efficiency of the engine is 20 percent \n" ] } ], "prompt_number": 11 } ], "metadata": {} } ] }