{"id":397,"date":"2023-10-02T17:52:15","date_gmt":"2023-10-02T17:52:15","guid":{"rendered":"https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/chapter\/exercise-4-changing-thermal-properties-of-peat-as-it-thaws\/"},"modified":"2023-11-29T14:15:05","modified_gmt":"2023-11-29T14:15:05","slug":"exercise-4-changing-thermal-properties-of-peat-as-it-thaws","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/chapter\/exercise-4-changing-thermal-properties-of-peat-as-it-thaws\/","title":{"raw":"Exercise 4 - Changing Thermal Properties of Peat as it Thaws","rendered":"Exercise 4 &#8211; Changing Thermal Properties of Peat as it Thaws"},"content":{"raw":"<p class=\"indent hanging-indent\">As a peat profile thaws, it changes state from being:<\/p>\r\n\r\n<ul id=\"l24\">\r\n \t<li data-list-text=\"\u2022\">\r\n<p class=\"indent hanging-indent\">saturated and frozen; to<\/p>\r\n<\/li>\r\n \t<li data-list-text=\"\u2022\">\r\n<p class=\"indent hanging-indent\">saturated and unfrozen; and then to<\/p>\r\n<\/li>\r\n \t<li data-list-text=\"\u2022\">\r\n<p class=\"indent hanging-indent\">unsaturated and unfrozen (in other words, the soil thaws, then drains).<\/p>\r\n<\/li>\r\n<\/ul>\r\n<ol id=\"l25\">\r\n \t<li data-list-text=\"1.\">The volumetric heat capacity (J m<sup><span class=\"s20\">-3<\/span><\/sup> C<sup><span class=\"s20\">-1<\/span><\/sup>) is the quantity of heat needed to raise the temperature of a unit volume of soil. Compute the values of the volumetric heat capacity of a peat soil for each of these three stages using the appropriate choice from the following equations.<\/li>\r\n<\/ol>\r\n<img class=\" wp-image-888 aligncenter\" src=\"https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-content\/uploads\/sites\/34\/2023\/10\/Screenshot-2023-11-06-at-1.11.57-PM-300x109.png\" alt=\"\" width=\"416\" height=\"151\" \/>\r\n<p class=\"import-Normal\" style=\"margin-left: 70.7pt; margin-right: 10.4pt; text-indent: 0pt;\"><img class=\"alignnone wp-image-1173\" src=\"https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-content\/uploads\/sites\/34\/2023\/10\/Screenshot-2023-11-20-at-4.51.11\u202fPM-300x225.png\" alt=\"\" width=\"372\" height=\"279\" \/><\/p>\r\nAssume the soil profile is entirely peat. The results of Hayashi and others (2007) suggest the liquid soil moisture content for frozen soil is in the range of 0.15 to 0.2 (assume 0.2 for this case) and the drained water content is 0.5. For each constituent, the values of specific heat, <em>cp<\/em> (J kg<sup>-1<\/sup> C<sup>-1<\/sup>), mass density, <em>\u03c1<\/em> (kg m<sup>-3<\/sup>), porosity, <em>\ud835\udf19<\/em><sub>t<\/sub> (-), and thermal conductivity, <em>k<\/em><sub><em>t<\/em><\/sub> (W m<sup>-1<\/sup> \u2103<sup>-1<\/sup>) are given in following table. Volumetric heat capacity is the product of specific heat capacity and density\r\n\r\n&nbsp;\r\n\r\n<img class=\" wp-image-1128 aligncenter\" src=\"https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-content\/uploads\/sites\/34\/2023\/10\/Screenshot-2023-11-19-at-4.45.09\u202fPM-300x85.png\" alt=\"\" width=\"730\" height=\"207\" \/>\r\n\r\n2. How would the transition from one condition to the next affect temperatures within the peat profile? What factors might effect the rate of transition from one condition to the next, and therefore the rate of temperature increases in the peat profile? For those who have access to commercial publications of the Wiley publishing house, Hayashi and others (2007) provides a thorough discussion of this topic.\r\n\r\n3. Another important thermal property of porous media is its thermal conductivity (W m<sup>-1<\/sup> \u2103<sup>-1<\/sup>), defined as the amount of heat transferred through a unit area per unit time under a unit temperature gradient. Considering the very large difference in thermal conductivity values presented in the table above, describe how the transition from one compositional stage to the next effects the rate of ground thaw.\r\n<p class=\"import-Normal\" style=\"text-align: right; margin-left: 0.5pt; margin-right: -0.65pt; text-indent: 0.5pt;\"><a href=\"https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/chapter\/solution-to-exercise-4\/\"><strong>Click for solution to Exercise 4<\/strong><\/a><\/p>","rendered":"<p class=\"indent hanging-indent\">As a peat profile thaws, it changes state from being:<\/p>\n<ul id=\"l24\">\n<li data-list-text=\"\u2022\">\n<p class=\"indent hanging-indent\">saturated and frozen; to<\/p>\n<\/li>\n<li data-list-text=\"\u2022\">\n<p class=\"indent hanging-indent\">saturated and unfrozen; and then to<\/p>\n<\/li>\n<li data-list-text=\"\u2022\">\n<p class=\"indent hanging-indent\">unsaturated and unfrozen (in other words, the soil thaws, then drains).<\/p>\n<\/li>\n<\/ul>\n<ol id=\"l25\">\n<li data-list-text=\"1.\">The volumetric heat capacity (J m<sup><span class=\"s20\">-3<\/span><\/sup> C<sup><span class=\"s20\">-1<\/span><\/sup>) is the quantity of heat needed to raise the temperature of a unit volume of soil. Compute the values of the volumetric heat capacity of a peat soil for each of these three stages using the appropriate choice from the following equations.<\/li>\n<\/ol>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-888 aligncenter\" src=\"https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-content\/uploads\/sites\/34\/2023\/10\/Screenshot-2023-11-06-at-1.11.57-PM-300x109.png\" alt=\"\" width=\"416\" height=\"151\" srcset=\"https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-content\/uploads\/sites\/34\/2023\/10\/Screenshot-2023-11-06-at-1.11.57-PM-300x109.png 300w, https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-content\/uploads\/sites\/34\/2023\/10\/Screenshot-2023-11-06-at-1.11.57-PM-768x279.png 768w, https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-content\/uploads\/sites\/34\/2023\/10\/Screenshot-2023-11-06-at-1.11.57-PM-65x24.png 65w, https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-content\/uploads\/sites\/34\/2023\/10\/Screenshot-2023-11-06-at-1.11.57-PM-225x82.png 225w, https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-content\/uploads\/sites\/34\/2023\/10\/Screenshot-2023-11-06-at-1.11.57-PM-350x127.png 350w, https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-content\/uploads\/sites\/34\/2023\/10\/Screenshot-2023-11-06-at-1.11.57-PM.png 924w\" sizes=\"auto, (max-width: 416px) 100vw, 416px\" \/><\/p>\n<p class=\"import-Normal\" style=\"margin-left: 70.7pt; margin-right: 10.4pt; text-indent: 0pt;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1173\" src=\"https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-content\/uploads\/sites\/34\/2023\/10\/Screenshot-2023-11-20-at-4.51.11\u202fPM-300x225.png\" alt=\"\" width=\"372\" height=\"279\" srcset=\"https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-content\/uploads\/sites\/34\/2023\/10\/Screenshot-2023-11-20-at-4.51.11\u202fPM-300x225.png 300w, https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-content\/uploads\/sites\/34\/2023\/10\/Screenshot-2023-11-20-at-4.51.11\u202fPM-1024x769.png 1024w, https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-content\/uploads\/sites\/34\/2023\/10\/Screenshot-2023-11-20-at-4.51.11\u202fPM-768x577.png 768w, https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-content\/uploads\/sites\/34\/2023\/10\/Screenshot-2023-11-20-at-4.51.11\u202fPM-1536x1154.png 1536w, https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-content\/uploads\/sites\/34\/2023\/10\/Screenshot-2023-11-20-at-4.51.11\u202fPM-65x49.png 65w, https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-content\/uploads\/sites\/34\/2023\/10\/Screenshot-2023-11-20-at-4.51.11\u202fPM-225x169.png 225w, https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-content\/uploads\/sites\/34\/2023\/10\/Screenshot-2023-11-20-at-4.51.11\u202fPM-350x263.png 350w, https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-content\/uploads\/sites\/34\/2023\/10\/Screenshot-2023-11-20-at-4.51.11\u202fPM.png 1592w\" sizes=\"auto, (max-width: 372px) 100vw, 372px\" \/><\/p>\n<p>Assume the soil profile is entirely peat. The results of Hayashi and others (2007) suggest the liquid soil moisture content for frozen soil is in the range of 0.15 to 0.2 (assume 0.2 for this case) and the drained water content is 0.5. For each constituent, the values of specific heat, <em>cp<\/em> (J kg<sup>-1<\/sup> C<sup>-1<\/sup>), mass density, <em>\u03c1<\/em> (kg m<sup>-3<\/sup>), porosity, <em>\ud835\udf19<\/em><sub>t<\/sub> (-), and thermal conductivity, <em>k<\/em><sub><em>t<\/em><\/sub> (W m<sup>-1<\/sup> \u2103<sup>-1<\/sup>) are given in following table. Volumetric heat capacity is the product of specific heat capacity and density<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1128 aligncenter\" src=\"https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-content\/uploads\/sites\/34\/2023\/10\/Screenshot-2023-11-19-at-4.45.09\u202fPM-300x85.png\" alt=\"\" width=\"730\" height=\"207\" srcset=\"https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-content\/uploads\/sites\/34\/2023\/10\/Screenshot-2023-11-19-at-4.45.09\u202fPM-300x85.png 300w, https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-content\/uploads\/sites\/34\/2023\/10\/Screenshot-2023-11-19-at-4.45.09\u202fPM-1024x289.png 1024w, https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-content\/uploads\/sites\/34\/2023\/10\/Screenshot-2023-11-19-at-4.45.09\u202fPM-768x217.png 768w, https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-content\/uploads\/sites\/34\/2023\/10\/Screenshot-2023-11-19-at-4.45.09\u202fPM-1536x434.png 1536w, https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-content\/uploads\/sites\/34\/2023\/10\/Screenshot-2023-11-19-at-4.45.09\u202fPM-2048x578.png 2048w, https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-content\/uploads\/sites\/34\/2023\/10\/Screenshot-2023-11-19-at-4.45.09\u202fPM-65x18.png 65w, https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-content\/uploads\/sites\/34\/2023\/10\/Screenshot-2023-11-19-at-4.45.09\u202fPM-225x64.png 225w, https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-content\/uploads\/sites\/34\/2023\/10\/Screenshot-2023-11-19-at-4.45.09\u202fPM-350x99.png 350w\" sizes=\"auto, (max-width: 730px) 100vw, 730px\" \/><\/p>\n<p>2. How would the transition from one condition to the next affect temperatures within the peat profile? What factors might effect the rate of transition from one condition to the next, and therefore the rate of temperature increases in the peat profile? For those who have access to commercial publications of the Wiley publishing house, Hayashi and others (2007) provides a thorough discussion of this topic.<\/p>\n<p>3. Another important thermal property of porous media is its thermal conductivity (W m<sup>-1<\/sup> \u2103<sup>-1<\/sup>), defined as the amount of heat transferred through a unit area per unit time under a unit temperature gradient. Considering the very large difference in thermal conductivity values presented in the table above, describe how the transition from one compositional stage to the next effects the rate of ground thaw.<\/p>\n<p class=\"import-Normal\" style=\"text-align: right; margin-left: 0.5pt; margin-right: -0.65pt; text-indent: 0.5pt;\"><a href=\"https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/chapter\/solution-to-exercise-4\/\"><strong>Click for solution to Exercise 4<\/strong><\/a><\/p>\n","protected":false},"author":6,"menu_order":4,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-397","chapter","type-chapter","status-publish","hentry"],"part":540,"_links":{"self":[{"href":"https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-json\/pressbooks\/v2\/chapters\/397","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-json\/wp\/v2\/users\/6"}],"version-history":[{"count":54,"href":"https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-json\/pressbooks\/v2\/chapters\/397\/revisions"}],"predecessor-version":[{"id":1349,"href":"https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-json\/pressbooks\/v2\/chapters\/397\/revisions\/1349"}],"part":[{"href":"https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-json\/pressbooks\/v2\/parts\/540"}],"metadata":[{"href":"https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-json\/pressbooks\/v2\/chapters\/397\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-json\/wp\/v2\/media?parent=397"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-json\/pressbooks\/v2\/chapter-type?post=397"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-json\/wp\/v2\/contributor?post=397"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/books.gw-project.org\/groundwater-in-peat-and-peatlands\/wp-json\/wp\/v2\/license?post=397"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}