{"id":652,"date":"2016-11-30T22:17:20","date_gmt":"2016-11-30T22:17:20","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/?post_type=chapter&#038;p=652"},"modified":"2019-05-30T16:31:28","modified_gmt":"2019-05-30T16:31:28","slug":"temperature-scales","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/chapter\/temperature-scales\/","title":{"raw":"Temperature Scales","rendered":"Temperature Scales"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Describe the general relationship between the U.S. customary units and metric units of length, weight\/mass, and volume<\/li>\r\n \t<li>Define the metric prefixes and use them to perform basic conversions among metric units<\/li>\r\n \t<li>Solve application problems using metric units<\/li>\r\n<\/ul>\r\n<ul>\r\n \t<li>State the freezing and boiling points of water on the Celsius and Fahrenheit temperature scales.<\/li>\r\n \t<li>Convert from one temperature scale to the other, using conversion formulas<\/li>\r\n<\/ul>\r\n<\/div>\r\nTurn on the television any morning and you will see meteorologists talking about the day\u0092s weather forecast. In addition to telling you what the weather conditions will be like (sunny, cloudy, rainy, muggy), they also tell you the day\u0092s forecast for high and low temperatures. A hot summer day may reach 100\u00b0 in Philadelphia, while a cool spring day may have a low of 40\u00b0 in Seattle.\r\n\r\nIf you have been to other countries, though, you may notice that meteorologists measure heat and cold differently outside of the United States. For example, a TV weatherman in San Diego may forecast a high of 89\u00b0, but a similar forecaster in Tijuana, Mexico\u0097, which is only 20 miles south\u0097, may look at the same weather pattern and say that the day\u0092's high temperature is going to be 32\u00b0. What\u0092s going on here? The difference is that the two countries use different temperature scales.\r\n<h2>Measuring Temperature on Two Scales<\/h2>\r\nFahrenheit and Celsius are two different scales for measuring temperature.\r\n<table border=\"0\" cellspacing=\"0\" cellpadding=\"0\">\r\n<tbody>\r\n<tr>\r\n<td>A thermometer measuring a temperature of 22\u00b0 Celsius is shown here.\r\n\r\nOn the Celsius scale, water freezes at 0\u00b0 and boils at 100\u00b0.\r\n\r\nIf the United States were to adopt the Celsius scale, forecast temperatures would rarely go below -30\u00b0 or above 45\u00b0. (A temperature of\r\n\r\n-18\u00b0 may be forecast for a cold winter day in Michigan, while a temperature of 43\u00b0 may be predicted for a hot summer day in Arizona.)\r\n\r\nMost office buildings maintain an indoor temperature between 18\u00b0C and 24\u00b0C to keep employees comfortable.<\/td>\r\n<td colspan=\"2\">\r\n<p style=\"text-align: center;\"><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30201023\/image109.jpg\" alt=\"Two thermometers, one measuring a temperature of 72 degrees Fahrenheit and the other measuring a temperature of 22 degrees Celsius. The boiling point of water (100 degrees Celsius and 212 degrees Fahrenheit) is shown on both themometers, as is the freezng point of water (0 degrees Celsius and 32 degrees Fahrenheit) and comfortable room temperature (18 to 25 degrees Celsius and 65 to 75 degrees Fahrenheit).\" width=\"224\" height=\"569\" \/><\/p>\r\n<\/td>\r\n<td>A thermometer measuring a temperature of 72\u00b0 Fahrenheit is shown here.\r\n\r\nOn the Fahrenheit scale, water freezes at 32\u00b0 and boils at 212\u00b0.\r\n\r\nIn the United States, forecast temperatures measured in Fahrenheit rarely go below -20\u00b0 or above 120\u00b0. (A temperature of 0\u00b0 may be forecast for a cold winter day in Michigan, while a temperature of 110\u00b0 may be predicted for a hot summer day in Arizona.)\r\n\r\nMost office buildings maintain an indoor temperature between 65\u00b0F and 75\u00b0F to keep employees comfortable.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><b>Celsius<\/b><\/td>\r\n<td>\r\n<p align=\"right\"><b>Fahrenheit<\/b><\/p>\r\n<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\nA cook puts a thermometer into a pot of water to see how hot it is. The thermometer reads 132\u00b0, but the water is not boiling yet. Which temperature scale is the thermometer measuring?\r\n\r\n<\/div>\r\n<h2>Converting Between the Scales<\/h2>\r\nBy looking at the two thermometers shown, you can make some general comparisons between the scales. For example, many people tend to be comfortable in outdoor temperatures between 50\u00b0F and 80\u00b0F (or between 10\u00b0C and 25\u00b0C). If a meteorologist predicts an average temperature of 0\u00b0C (or 32\u00b0F), then it is a safe bet that you will need a winter jacket.\r\n\r\nSometimes, it is necessary to convert a Celsius measurement to its exact Fahrenheit measurement or vice versa. For example, what if you want to know the temperature of your child in Fahrenheit, and the only thermometer you have measures temperature in Celsius measurement? Converting temperature between the systems is a straightforward process as long as you use the formulas provided below.\r\n<div class=\"textbox\">\r\n<h3>Temperature Conversion Formulas<\/h3>\r\nTo convert a Fahrenheit measurement to a Celsius measurement, use this formula.\r\n<p style=\"text-align: center;\">[latex] C=\\frac{5}{9}(F-32)[\/latex]<\/p>\r\nTo convert a Celsius measurement to a Fahrenheit measurement, use this formula.\r\n<p style=\"text-align: center;\">[latex] F=\\frac{9}{5}C+32[\/latex]<\/p>\r\n\r\n<\/div>\r\nHow were these formulas developed? They came from comparing the two scales. Since the freezing point is 0\u00b0 in the Celsius scale and 32\u00b0 on the Fahrenheit scale, we subtract 32 when converting from Fahrenheit to Celsius, and add 32 when converting from Celsius to Fahrenheit.\r\n\r\nThere is a reason for the fractions [latex] \\frac{5}{9}[\/latex] and [latex] \\frac{9}{5}[\/latex], also. There are 100 degrees between the freezing (0\u00b0) and boiling points (100\u00b0) of water on the Celsius scale and 180 degrees between the similar points (32\u00b0 and 212\u00b0) on the Fahrenheit scale. Writing these two scales as a ratio, [latex] \\frac{F{}^\\circ }{C{}^\\circ }[\/latex], gives [latex] \\frac{180{}^\\circ }{100{}^\\circ }=\\frac{180{}^\\circ \\div 20}{100{}^\\circ \\div 20}=\\frac{9}{5}[\/latex]. If you flip the ratio to be [latex] \\frac{\\text{C}{}^\\circ }{\\text{F}{}^\\circ }[\/latex], you get [latex] \\frac{100{}^\\circ }{180{}^\\circ }=\\frac{100{}^\\circ \\div 20}{180{}^\\circ \\div 20}=\\frac{5}{9}[\/latex]. Notice how these fractions are used in the conversion formulas.\r\n\r\nThe example below illustrates the conversion of Celsius temperature to Fahrenheit temperature, using the boiling point of water, which is 100\u00b0 C.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nThe boiling point of water is 100\u00b0C. What temperature does water boil at in the Fahrenheit scale?\r\n\r\nA Celsius temperature is given. To convert it to the Fahrenheit scale, use the formula at the left.\r\n<p style=\"text-align: center;\">[latex]F=\\frac{9}{5}C+32[\/latex]<\/p>\r\nSubstitute 100 for <i>C<\/i> and multiply.\r\n<p style=\"text-align: center;\">[latex]F=\\frac{9}{5}(100)+32[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]F=\\frac{900}{5}+32[\/latex]<\/p>\r\nSimplify [latex]\\frac{900}{5}[\/latex] by dividing numerator and denominator by 5.\r\n<p style=\"text-align: center;\">[latex]F=\\frac{900\\div 5}{5\\div 5}+32[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]F=\\frac{180}{1}+32[\/latex]<\/p>\r\nAdd [latex]180+32[\/latex].\r\n<p style=\"text-align: center;\" align=\"right\">[latex]F=212[\/latex]<\/p>\r\nThe boiling point of water is 212\u00b0F.\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n<iframe id=\"mom1\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=1011&amp;theme=oea&amp;iframe_resize_id=mom1\" width=\"100%\" height=\"250\"><\/iframe>\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nWater freezes at 32\u00b0F. On the Celsius scale, what temperature is this?\r\n\r\n[reveal-answer q=\"825354\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"825354\"]\r\n\r\nA Fahrenheit temperature is given. To convert it to the Celsius scale, use the formula at the left.\r\n<p style=\"text-align: center;\" align=\"right\">[latex] C=\\frac{5}{9}(F-32)[\/latex]<\/p>\r\nSubstitute 32 for <i>F<\/i> and subtract.\r\n<p style=\"text-align: center;\" align=\"right\">[latex] C=\\frac{5}{9}(32-32)[\/latex]<\/p>\r\nAny number multiplied by 0 is 0.\r\n<p style=\"text-align: center;\" align=\"right\">[latex] C=\\frac{5}{9}(0)[\/latex]<\/p>\r\n<p style=\"text-align: center;\" align=\"right\">[latex] C=0[\/latex]<\/p>\r\nThe freezing point of water is [latex]0^{\\circ}\\text{C}[\/latex].\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n<iframe id=\"mom2\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=1010&amp;theme=oea&amp;iframe_resize_id=mom2\" width=\"100%\" height=\"250\"><\/iframe>\r\n\r\n<\/div>\r\nThe two previous problems used the conversion formulas to verify some temperature conversions that were discussed earlier\u0097the boiling and freezing points of water. The next example shows how these formulas can be used to solve a real-world problem using different temperature scales.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nTwo scientists are doing an experiment designed to identify the boiling point of an unknown liquid. One scientist gets a result of 120\u00b0C; the other gets a result of 250\u00b0F. Which temperature is higher and by how much?\r\n\r\n[reveal-answer q=\"607680\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"607680\"]\r\n\r\nOne temperature is given in \u00b0C, and the other is given in \u00b0F. To find the difference between them, we need to measure them on the same scale.\r\n\r\nWhat is the difference between 120\u00b0C and 250\u00b0F?\r\n\r\nUse the conversion formula to convert 120\u00b0C to \u00b0F.\r\n\r\n(You could convert 250\u00b0F to \u00b0C instead; this is explained in the text after this example.)\r\n<p style=\"text-align: center;\">[latex] F=\\frac{9}{5}C+32[\/latex]<\/p>\r\nSubstitute 120 for <i>C<\/i>.\r\n<p style=\"text-align: center;\">[latex] F=\\frac{9}{5}(120)+32[\/latex]<\/p>\r\nMultiply.\r\n<p style=\"text-align: center;\">[latex] F=\\frac{1080}{5}+32[\/latex]<\/p>\r\nSimplify [latex] \\frac{1080}{5}[\/latex] by dividing numerator and denominator by 5.\r\n<p style=\"text-align: center;\">[latex] F=\\frac{1080\\div 5}{5\\div 5}+32[\/latex]<\/p>\r\nAdd [latex]216+32[\/latex].\r\n<p style=\"text-align: center;\">[latex] F=\\frac{216}{1}+32[\/latex]<\/p>\r\nYou have found that [latex]120^{\\circ}\\text{C}=248^{\\circ}\\text{F}[\/latex].\r\n<p style=\"text-align: center;\">[latex] F=248[\/latex]<\/p>\r\nTo find the difference between 248\u00b0<i>F<\/i> and 250\u00b0F, subtract.\r\n<p style=\"text-align: center;\">[latex]250^{\\circ}\\text{F}-248^{\\circ}\\text{F}=2^{\\circ}\\text{F}[\/latex]<\/p>\r\n250\u00b0F is the higher temperature by 2\u00b0F.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nYou could have converted 250\u00b0F to \u00b0C instead, and then found the difference in the two measurements. (Had you done it this way, you would have found that [latex]250^{\\circ}\\text{F}=121.1^{\\circ}\\text{C}[\/latex], and that 121.1\u00b0C is 1.1\u00b0C higher than 120\u00b0C.) Whichever way you choose, it is important to compare the temperature measurements within the same scale, and to apply the conversion formulas accurately.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\nTatiana is researching vacation destinations, and she sees that the average summer temperature in Barcelona, Spain is around 26\u00b0C. What is the average temperature in degrees Fahrenheit?\r\n\r\n<\/div>\r\n<h2>Summary<\/h2>\r\nTemperature is often measured in one of two scales: the Celsius scale and the Fahrenheit scale. A Celsius thermometer will measure the boiling point of water at 100\u00b0 and its freezing point at 0\u00b0; a Fahrenheit thermometer will measure the same events at 212\u00b0 for the boiling point of water and 32\u00b0 as its freezing point. You can use conversion formulas to convert a measurement made in one scale to the other scale.","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Describe the general relationship between the U.S. customary units and metric units of length, weight\/mass, and volume<\/li>\n<li>Define the metric prefixes and use them to perform basic conversions among metric units<\/li>\n<li>Solve application problems using metric units<\/li>\n<\/ul>\n<ul>\n<li>State the freezing and boiling points of water on the Celsius and Fahrenheit temperature scales.<\/li>\n<li>Convert from one temperature scale to the other, using conversion formulas<\/li>\n<\/ul>\n<\/div>\n<p>Turn on the television any morning and you will see meteorologists talking about the day\u0092s weather forecast. In addition to telling you what the weather conditions will be like (sunny, cloudy, rainy, muggy), they also tell you the day\u0092s forecast for high and low temperatures. A hot summer day may reach 100\u00b0 in Philadelphia, while a cool spring day may have a low of 40\u00b0 in Seattle.<\/p>\n<p>If you have been to other countries, though, you may notice that meteorologists measure heat and cold differently outside of the United States. For example, a TV weatherman in San Diego may forecast a high of 89\u00b0, but a similar forecaster in Tijuana, Mexico\u0097, which is only 20 miles south\u0097, may look at the same weather pattern and say that the day\u0092&#8217;s high temperature is going to be 32\u00b0. What\u0092s going on here? The difference is that the two countries use different temperature scales.<\/p>\n<h2>Measuring Temperature on Two Scales<\/h2>\n<p>Fahrenheit and Celsius are two different scales for measuring temperature.<\/p>\n<table cellpadding=\"0\" style=\"border-spacing: 0px;\">\n<tbody>\n<tr>\n<td>A thermometer measuring a temperature of 22\u00b0 Celsius is shown here.<\/p>\n<p>On the Celsius scale, water freezes at 0\u00b0 and boils at 100\u00b0.<\/p>\n<p>If the United States were to adopt the Celsius scale, forecast temperatures would rarely go below -30\u00b0 or above 45\u00b0. (A temperature of<\/p>\n<p>-18\u00b0 may be forecast for a cold winter day in Michigan, while a temperature of 43\u00b0 may be predicted for a hot summer day in Arizona.)<\/p>\n<p>Most office buildings maintain an indoor temperature between 18\u00b0C and 24\u00b0C to keep employees comfortable.<\/td>\n<td colspan=\"2\">\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30201023\/image109.jpg\" alt=\"Two thermometers, one measuring a temperature of 72 degrees Fahrenheit and the other measuring a temperature of 22 degrees Celsius. The boiling point of water (100 degrees Celsius and 212 degrees Fahrenheit) is shown on both themometers, as is the freezng point of water (0 degrees Celsius and 32 degrees Fahrenheit) and comfortable room temperature (18 to 25 degrees Celsius and 65 to 75 degrees Fahrenheit).\" width=\"224\" height=\"569\" \/><\/p>\n<\/td>\n<td>A thermometer measuring a temperature of 72\u00b0 Fahrenheit is shown here.<\/p>\n<p>On the Fahrenheit scale, water freezes at 32\u00b0 and boils at 212\u00b0.<\/p>\n<p>In the United States, forecast temperatures measured in Fahrenheit rarely go below -20\u00b0 or above 120\u00b0. (A temperature of 0\u00b0 may be forecast for a cold winter day in Michigan, while a temperature of 110\u00b0 may be predicted for a hot summer day in Arizona.)<\/p>\n<p>Most office buildings maintain an indoor temperature between 65\u00b0F and 75\u00b0F to keep employees comfortable.<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><b>Celsius<\/b><\/td>\n<td>\n<p style=\"text-align: right;\"><b>Fahrenheit<\/b><\/p>\n<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p>A cook puts a thermometer into a pot of water to see how hot it is. The thermometer reads 132\u00b0, but the water is not boiling yet. Which temperature scale is the thermometer measuring?<\/p>\n<\/div>\n<h2>Converting Between the Scales<\/h2>\n<p>By looking at the two thermometers shown, you can make some general comparisons between the scales. For example, many people tend to be comfortable in outdoor temperatures between 50\u00b0F and 80\u00b0F (or between 10\u00b0C and 25\u00b0C). If a meteorologist predicts an average temperature of 0\u00b0C (or 32\u00b0F), then it is a safe bet that you will need a winter jacket.<\/p>\n<p>Sometimes, it is necessary to convert a Celsius measurement to its exact Fahrenheit measurement or vice versa. For example, what if you want to know the temperature of your child in Fahrenheit, and the only thermometer you have measures temperature in Celsius measurement? Converting temperature between the systems is a straightforward process as long as you use the formulas provided below.<\/p>\n<div class=\"textbox\">\n<h3>Temperature Conversion Formulas<\/h3>\n<p>To convert a Fahrenheit measurement to a Celsius measurement, use this formula.<\/p>\n<p style=\"text-align: center;\">[latex]C=\\frac{5}{9}(F-32)[\/latex]<\/p>\n<p>To convert a Celsius measurement to a Fahrenheit measurement, use this formula.<\/p>\n<p style=\"text-align: center;\">[latex]F=\\frac{9}{5}C+32[\/latex]<\/p>\n<\/div>\n<p>How were these formulas developed? They came from comparing the two scales. Since the freezing point is 0\u00b0 in the Celsius scale and 32\u00b0 on the Fahrenheit scale, we subtract 32 when converting from Fahrenheit to Celsius, and add 32 when converting from Celsius to Fahrenheit.<\/p>\n<p>There is a reason for the fractions [latex]\\frac{5}{9}[\/latex] and [latex]\\frac{9}{5}[\/latex], also. There are 100 degrees between the freezing (0\u00b0) and boiling points (100\u00b0) of water on the Celsius scale and 180 degrees between the similar points (32\u00b0 and 212\u00b0) on the Fahrenheit scale. Writing these two scales as a ratio, [latex]\\frac{F{}^\\circ }{C{}^\\circ }[\/latex], gives [latex]\\frac{180{}^\\circ }{100{}^\\circ }=\\frac{180{}^\\circ \\div 20}{100{}^\\circ \\div 20}=\\frac{9}{5}[\/latex]. If you flip the ratio to be [latex]\\frac{\\text{C}{}^\\circ }{\\text{F}{}^\\circ }[\/latex], you get [latex]\\frac{100{}^\\circ }{180{}^\\circ }=\\frac{100{}^\\circ \\div 20}{180{}^\\circ \\div 20}=\\frac{5}{9}[\/latex]. Notice how these fractions are used in the conversion formulas.<\/p>\n<p>The example below illustrates the conversion of Celsius temperature to Fahrenheit temperature, using the boiling point of water, which is 100\u00b0 C.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>The boiling point of water is 100\u00b0C. What temperature does water boil at in the Fahrenheit scale?<\/p>\n<p>A Celsius temperature is given. To convert it to the Fahrenheit scale, use the formula at the left.<\/p>\n<p style=\"text-align: center;\">[latex]F=\\frac{9}{5}C+32[\/latex]<\/p>\n<p>Substitute 100 for <i>C<\/i> and multiply.<\/p>\n<p style=\"text-align: center;\">[latex]F=\\frac{9}{5}(100)+32[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]F=\\frac{900}{5}+32[\/latex]<\/p>\n<p>Simplify [latex]\\frac{900}{5}[\/latex] by dividing numerator and denominator by 5.<\/p>\n<p style=\"text-align: center;\">[latex]F=\\frac{900\\div 5}{5\\div 5}+32[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]F=\\frac{180}{1}+32[\/latex]<\/p>\n<p>Add [latex]180+32[\/latex].<\/p>\n<p style=\"text-align: center; text-align: right;\">[latex]F=212[\/latex]<\/p>\n<p>The boiling point of water is 212\u00b0F.<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"mom1\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=1011&amp;theme=oea&amp;iframe_resize_id=mom1\" width=\"100%\" height=\"250\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Water freezes at 32\u00b0F. On the Celsius scale, what temperature is this?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q825354\">Show Solution<\/span><\/p>\n<div id=\"q825354\" class=\"hidden-answer\" style=\"display: none\">\n<p>A Fahrenheit temperature is given. To convert it to the Celsius scale, use the formula at the left.<\/p>\n<p style=\"text-align: center; text-align: right;\">[latex]C=\\frac{5}{9}(F-32)[\/latex]<\/p>\n<p>Substitute 32 for <i>F<\/i> and subtract.<\/p>\n<p style=\"text-align: center; text-align: right;\">[latex]C=\\frac{5}{9}(32-32)[\/latex]<\/p>\n<p>Any number multiplied by 0 is 0.<\/p>\n<p style=\"text-align: center; text-align: right;\">[latex]C=\\frac{5}{9}(0)[\/latex]<\/p>\n<p style=\"text-align: center; text-align: right;\">[latex]C=0[\/latex]<\/p>\n<p>The freezing point of water is [latex]0^{\\circ}\\text{C}[\/latex].<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"mom2\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=1010&amp;theme=oea&amp;iframe_resize_id=mom2\" width=\"100%\" height=\"250\"><\/iframe><\/p>\n<\/div>\n<p>The two previous problems used the conversion formulas to verify some temperature conversions that were discussed earlier\u0097the boiling and freezing points of water. The next example shows how these formulas can be used to solve a real-world problem using different temperature scales.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Two scientists are doing an experiment designed to identify the boiling point of an unknown liquid. One scientist gets a result of 120\u00b0C; the other gets a result of 250\u00b0F. Which temperature is higher and by how much?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q607680\">Show Solution<\/span><\/p>\n<div id=\"q607680\" class=\"hidden-answer\" style=\"display: none\">\n<p>One temperature is given in \u00b0C, and the other is given in \u00b0F. To find the difference between them, we need to measure them on the same scale.<\/p>\n<p>What is the difference between 120\u00b0C and 250\u00b0F?<\/p>\n<p>Use the conversion formula to convert 120\u00b0C to \u00b0F.<\/p>\n<p>(You could convert 250\u00b0F to \u00b0C instead; this is explained in the text after this example.)<\/p>\n<p style=\"text-align: center;\">[latex]F=\\frac{9}{5}C+32[\/latex]<\/p>\n<p>Substitute 120 for <i>C<\/i>.<\/p>\n<p style=\"text-align: center;\">[latex]F=\\frac{9}{5}(120)+32[\/latex]<\/p>\n<p>Multiply.<\/p>\n<p style=\"text-align: center;\">[latex]F=\\frac{1080}{5}+32[\/latex]<\/p>\n<p>Simplify [latex]\\frac{1080}{5}[\/latex] by dividing numerator and denominator by 5.<\/p>\n<p style=\"text-align: center;\">[latex]F=\\frac{1080\\div 5}{5\\div 5}+32[\/latex]<\/p>\n<p>Add [latex]216+32[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]F=\\frac{216}{1}+32[\/latex]<\/p>\n<p>You have found that [latex]120^{\\circ}\\text{C}=248^{\\circ}\\text{F}[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]F=248[\/latex]<\/p>\n<p>To find the difference between 248\u00b0<i>F<\/i> and 250\u00b0F, subtract.<\/p>\n<p style=\"text-align: center;\">[latex]250^{\\circ}\\text{F}-248^{\\circ}\\text{F}=2^{\\circ}\\text{F}[\/latex]<\/p>\n<p>250\u00b0F is the higher temperature by 2\u00b0F.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>You could have converted 250\u00b0F to \u00b0C instead, and then found the difference in the two measurements. (Had you done it this way, you would have found that [latex]250^{\\circ}\\text{F}=121.1^{\\circ}\\text{C}[\/latex], and that 121.1\u00b0C is 1.1\u00b0C higher than 120\u00b0C.) Whichever way you choose, it is important to compare the temperature measurements within the same scale, and to apply the conversion formulas accurately.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p>Tatiana is researching vacation destinations, and she sees that the average summer temperature in Barcelona, Spain is around 26\u00b0C. What is the average temperature in degrees Fahrenheit?<\/p>\n<\/div>\n<h2>Summary<\/h2>\n<p>Temperature is often measured in one of two scales: the Celsius scale and the Fahrenheit scale. A Celsius thermometer will measure the boiling point of water at 100\u00b0 and its freezing point at 0\u00b0; a Fahrenheit thermometer will measure the same events at 212\u00b0 for the boiling point of water and 32\u00b0 as its freezing point. You can use conversion formulas to convert a measurement made in one scale to the other scale.<\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-652\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Revision and Adaptation. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Question ID 1011, 1010. <strong>Authored by<\/strong>: Lippman, David. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: IMathAS Community License CC-BY + GPL<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":21,"menu_order":9,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Question ID 1011, 1010\",\"author\":\"Lippman, David\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"IMathAS Community License CC-BY + GPL\"},{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"c80ca3f8-44d0-4faf-be00-fd15c72fdaeb","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-652","chapter","type-chapter","status-publish","hentry"],"part":658,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/chapters\/652","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/wp\/v2\/users\/21"}],"version-history":[{"count":16,"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/chapters\/652\/revisions"}],"predecessor-version":[{"id":2960,"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/chapters\/652\/revisions\/2960"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/parts\/658"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/chapters\/652\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/wp\/v2\/media?parent=652"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/chapter-type?post=652"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/wp\/v2\/contributor?post=652"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/wp\/v2\/license?post=652"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}