{"id":607,"date":"2016-04-20T22:24:54","date_gmt":"2016-04-21T03:24:54","guid":{"rendered":"http:\/\/rpchurchill.com\/?p=607"},"modified":"2017-02-04T17:14:36","modified_gmt":"2017-02-04T22:14:36","slug":"extending-the-thermodynamic-functions-to-their-full-range","status":"publish","type":"post","link":"https:\/\/rpchurchill.com\/wordpress\/posts\/2016\/04\/20\/extending-the-thermodynamic-functions-to-their-full-range\/","title":{"rendered":"Extending the Thermodynamic Functions To Their Full Range"},"content":{"rendered":"<p>Today I extended all 24 functions to their full range, 0-705.44 \u00b0F and 0.08866-3203.6 psi. I&#8217;ve shown the functions vs. temperature; the functions vs. pressure are generally derived from the same lines in the steam tables so the only difference would be the values and units on the x-axis.<\/p>\n<p>One problem that comes up is how to deal with endpoints or local extreme values. Continuous functions are written out pixel by pixel along the x-axis, so if the value chosen doesn&#8217;t happen to fall right on an endpoint or a local high or low value then part of the curve won&#8217;t be drawn. I&#8217;ve finessed this for today by defining the endpoints of the x-axis to coincide with the exact high and low values of the input range (i.e., the x-axis, with some tweaking by hand at the high end), which really isn&#8217;t satisfactory. I can think of a few things I might do but none make me very happy. I&#8217;m going to have to do some research and think about it a little more.<\/p>\n<p>In the meantime, here are the full plots vs. temperature, and the plot of temperature vs. pressure as a representative example.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.rpchurchill.com\/images\/articles\/Tfind_P_full.png\" alt=\"\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.rpchurchill.com\/images\/articles\/Tfind_v_f_full.png\" alt=\"\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.rpchurchill.com\/images\/articles\/Tfind_v_g_full.png\" alt=\"\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.rpchurchill.com\/images\/articles\/Tfind_u_f_full.png\" alt=\"\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.rpchurchill.com\/images\/articles\/Tfind_u_fg_full.png\" alt=\"\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.rpchurchill.com\/images\/articles\/Tfind_u_g_full.png\" alt=\"\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.rpchurchill.com\/images\/articles\/Tfind_h_f_full.png\" alt=\"\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.rpchurchill.com\/images\/articles\/Tfind_h_fg_full.png\" alt=\"\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.rpchurchill.com\/images\/articles\/Tfind_h_g_full.png\" alt=\"\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.rpchurchill.com\/images\/articles\/Tfind_s_f_full.png\" alt=\"\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.rpchurchill.com\/images\/articles\/Tfind_s_fg_full.png\" alt=\"\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.rpchurchill.com\/images\/articles\/Tfind_s_g_full.png\" alt=\"\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.rpchurchill.com\/images\/articles\/Pfind_T_full.png\" alt=\"\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Today I extended all 24 functions to their full range, 0-705.44 \u00b0F and 0.08866-3203.6 psi. I&#8217;ve shown the functions vs. temperature; the functions vs. pressure are generally derived from the same lines in the steam tables so the only difference &hellip; <a href=\"https:\/\/rpchurchill.com\/wordpress\/posts\/2016\/04\/20\/extending-the-thermodynamic-functions-to-their-full-range\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[14],"tags":[79,84,77],"_links":{"self":[{"href":"https:\/\/rpchurchill.com\/wordpress\/wp-json\/wp\/v2\/posts\/607"}],"collection":[{"href":"https:\/\/rpchurchill.com\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/rpchurchill.com\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/rpchurchill.com\/wordpress\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/rpchurchill.com\/wordpress\/wp-json\/wp\/v2\/comments?post=607"}],"version-history":[{"count":4,"href":"https:\/\/rpchurchill.com\/wordpress\/wp-json\/wp\/v2\/posts\/607\/revisions"}],"predecessor-version":[{"id":1517,"href":"https:\/\/rpchurchill.com\/wordpress\/wp-json\/wp\/v2\/posts\/607\/revisions\/1517"}],"wp:attachment":[{"href":"https:\/\/rpchurchill.com\/wordpress\/wp-json\/wp\/v2\/media?parent=607"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/rpchurchill.com\/wordpress\/wp-json\/wp\/v2\/categories?post=607"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/rpchurchill.com\/wordpress\/wp-json\/wp\/v2\/tags?post=607"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}