{"id":2241,"date":"2024-08-04T13:23:20","date_gmt":"2024-08-04T13:23:20","guid":{"rendered":"https:\/\/workhouse.sweetdishy.com\/?p=2241"},"modified":"2024-08-04T13:23:21","modified_gmt":"2024-08-04T13:23:21","slug":"specific-heats-of-gases","status":"publish","type":"post","link":"https:\/\/workhouse.sweetdishy.com\/index.php\/2024\/08\/04\/specific-heats-of-gases\/","title":{"rendered":"Specific heats of gases"},"content":{"rendered":"\n<p>Specific heats of gases<\/p>\n\n\n\n<p><a><\/a><em>Specific heat at constant pressure<\/em>,&nbsp;<em>c<\/em><sub>p<\/sub>. This is the quantity of heat energy supplied to raise 1 kg of the gas through 1\u00b0C or K, while the gas is at constant pressure.<\/p>\n\n\n\n<p><a><\/a>Think of 1 kg of gas trapped in a cylinder. As heat energy is added, the pressure will rise. If the piston is allowed to move down the cylinder to prevent the rise in pressure, the amount of heat energy supplied to raise the temperature of the gas by 1\u00b0C is the specific heat of the gas at constant pressure.<\/p>\n\n\n\n<p><a><\/a><em>Specific heat at constant volume<\/em>,&nbsp;<em>c<\/em><sub>v<\/sub>. This is the quantity of heat energy supplied to raise 1 kg of the gas through 1\u00b0C or K, while the gas is at constant volume.<\/p>\n\n\n\n<p><a><\/a>Thinking again of the gas in the cylinder, in this case the heat energy is supplied while the piston is fixed, i.e. the volume is constant. The amount of heat energy added for the temperature to rise 1\u00b0C is the specific heat at constant volume,&nbsp;<em>c<\/em><sub>v<\/sub>.<\/p>\n\n\n\n<p><a><\/a>The specific heat of a gas at constant pressure is always a higher value than the specific heat at constant volume, because when the gas is receiving heat it must be allowed to expand to prevent a rise in pressure, and, while expanding, the gas is doing work in driving the piston down the cylinder. Extra heat energy must be supplied equivalent to the work done.<\/p>\n\n\n\n<p><a><\/a>Note that this is an example of the equivalence of heat energy and work energy.<\/p>\n\n\n\n<p>Example 2.1.3<\/p>\n\n\n\n<p><a><\/a>1.5 kg of gas at 20\u00b0C is contained in a cylinder and heated to 75\u00b0C while the volume remains constant. Calculate the heat energy supplied if&nbsp;<em>c<\/em><sub>v<\/sub>&nbsp;= 700 J\/kgK.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9780750652131\/files\/images\/B9780750652131500027_si7.gif\" alt=\"image\"\/><\/figure>\n\n\n\n<p>Example 2.1.4<\/p>\n\n\n\n<p><a><\/a><a><\/a>A gas with a specific heat at constant pressure,&nbsp;<em>c<\/em><sub>p<\/sub>&nbsp;= 900 J\/kgK, is supplied with 80 kJ of heat energy. If the mass of the gas is 2 kg and its initial temperature is 10\u00b0C, find the final temperature of the gas if it is heated at constant pressure.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9780750652131\/files\/images\/B9780750652131500027_si8.gif\" alt=\"image\"\/><\/figure>\n\n\n\n<p><a><\/a>Final temperature = 10 + 44.44 =&nbsp;54.44\u00b0C<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Specific heats of gases Specific heat at constant pressure,&nbsp;cp. This is the quantity of heat energy supplied to raise 1 kg of the gas through 1\u00b0C or K, while the gas is at constant pressure. Think of 1 kg of gas trapped in a cylinder. As heat energy is added, the pressure will rise. If [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":2236,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[373],"tags":[],"class_list":["post-2241","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-thermodynamics"],"jetpack_featured_media_url":"https:\/\/workhouse.sweetdishy.com\/wp-content\/uploads\/2024\/08\/download-22.png","_links":{"self":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2241","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/comments?post=2241"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2241\/revisions"}],"predecessor-version":[{"id":2242,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2241\/revisions\/2242"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media\/2236"}],"wp:attachment":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media?parent=2241"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=2241"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=2241"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}