{"id":4671,"date":"2024-10-03T19:57:10","date_gmt":"2024-10-03T19:57:10","guid":{"rendered":"https:\/\/workhouse.sweetdishy.com\/?p=4671"},"modified":"2024-10-03T19:57:11","modified_gmt":"2024-10-03T19:57:11","slug":"enthalpy-and-heat-capacity","status":"publish","type":"post","link":"https:\/\/workhouse.sweetdishy.com\/index.php\/2024\/10\/03\/enthalpy-and-heat-capacity\/","title":{"rendered":"\u00a0Enthalpy and Heat Capacity"},"content":{"rendered":"\n

Enthalpy is a measure of the energy (or heat) content of a substance [3]. It is a thermodynamic quantity whose\u00a0absolute<\/em>\u00a0value cannot be determined; however, enthalpy of a substance with respect to its value at some reference conditions can be calculated [4,\u00a05]. The reference state, also called the\u00a0standard state,<\/em>\u00a0is\u00a0specified in terms of pressure and temperature of the system, usually 1 bar and 25\u00b0C (298.15 K) [6]. The standard specific enthalpies (enthalpy per mole) of formation of various substances (from its constituent elements) at the reference state are available from various sources, including books on thermodynamics [3], handbooks [7], and Web databases such the one maintained by the National Institute of Standards and Technology (www.nist.gov).4<\/sup>\u00a0Thus, the specific enthalpy of any substance at any other condition can be calculated from its functional dependence on system variables and the reference state enthalpy.<\/p>\n\n\n\n

4.\u00a0By convention, the enthalpies of formation of elements in their natural states of occurrence are taken to be zero.<\/p>\n\n\n\n

Enthalpy is a function of temperature and pressure of the system, and its dependence on temperature at constant pressure is described as follows:<\/p>\n\n\n\n

\"Image\"\/<\/figure>\n\n\n\n

The left side of this equation represents the partial derivative of enthalpy with respect to temperature at constant pressure; h<\/em> is the specific enthalpy of the substance\u2014that is, enthalpy per unit mole\u2014and CP<\/sub><\/em> is the specific heat capacity of the substance at constant pressure. The SI units of h<\/em> and CP<\/sub><\/em> are joule per mole (J\/mol) and joule per mole per kelvin (J\/mol K), respectively. The specific enthalpy h<\/em> does not depend on the quantity of substance present, making it an intensive<\/em> property. The total enthalpy H<\/em>, on the other hand, is an extensive<\/em> property, which depends on the quantity of material present in the system.5<\/a><\/sup> H<\/em> is obtained simply by multiplying the specific enthalpy by the number of moles present and has the unit of J (joule).<\/p>\n\n\n\n

5.\u00a0The intensive and extensive properties are discussed in detail in the thermodynamics courses.<\/p>\n\n\n\n

If the information about the specific heat capacity\u00a0CP<\/sub><\/em>\u00a0is available, then integration of\u00a0equation 7.6\u00a0enables us to calculate the change in enthalpy (\u0394h<\/em>) when the temperature of the substance changes from\u00a0T<\/em>1<\/sub>\u00a0to\u00a0T<\/em>2<\/sub>\u00a0at constant pressure:<\/p>\n\n\n\n

\"Image\"\/<\/figure>\n\n\n\n

where h<\/em>1<\/sub> and h<\/em>2<\/sub> are the specific enthalpies of the substance at the temperatures T<\/em>1<\/sub> and T<\/em>2<\/sub>, respectively.<\/p>\n\n\n\n

Note that\u00a0equation 7.7\u00a0is valid only when\u00a0CP<\/sub><\/em>, the specific heat capacity at constant pressure, does not depend on the temperature and hence is constant\u00a0over the temperature range under consideration. Typically, however,\u00a0CP<\/sub><\/em>\u00a0is a function of temperature, the dependence often being expressed as polynomial in\u00a0T<\/em>, with one such function shown by\u00a0equation 7.8\u00a0[5].<\/p>\n\n\n\n

\"Image\"\/<\/figure>\n\n\n\n

Coefficients\u00a0A<\/em>\u00a0through\u00a0E<\/em>\u00a0are constants characteristic of the substance and are available from the same sources previously stated. The enthalpy change per unit mole of the substance is then calculated by integrating\u00a0equation 7.6:<\/p>\n\n\n\n

\"Image\"\/<\/figure>\n\n\n\n

Equation 7.7<\/a> or 7.9 is used for calculating the change in the specific enthalpy of a substance when its temperature changes from T<\/em>1<\/sub> to T<\/em>2<\/sub> under constant pressure conditions. When the process is not conducted under constant pressure (isobaric) conditions, enthalpy dependence on pressure also needs to be taken into account while performing the energy balance computations. The pressure dependence of enthalpy is complex and requires an understanding of the volumetric behavior of the substances\u2014that is, an understanding of the relationship between pressure, volume, and temperature for the substance. This is generally covered in the thermodynamics courses and is not considered in this text.<\/p>\n\n\n\n

The assumption implicit in the development of\u00a0equations 7.7\u00a0and\u00a07.9\u00a0is that the substance\u00a0does not undergo a phase change<\/em>; that is, it does not change its state from solid to liquid or liquid to gas, and vice versa. Thus, the substance undergoes only a\u00a0sensible heat change<\/em>\u00a0that is reflected in the temperature of the substance. However, if the substance does experience a phase change at a temperature intermediate between\u00a0T<\/em>1<\/sub>\u00a0and\u00a0T<\/em>2<\/sub>, then the enthalpy change should include a\u00a0latent heat<\/em>\u00a0component. For example, if the boiling point of the substance\u00a0Tb<\/sub><\/em>\u00a0is greater than\u00a0T<\/em>1<\/sub>\u00a0but less than\u00a0T<\/em>2<\/sub>, then the substance is a liquid at the beginning of the process at\u00a0T<\/em>1<\/sub>, but at\u00a0T<\/em>2<\/sub>, at the end of the process, it is a vapor. The enthalpy change for this situation is described by\u00a0equation 7.10.<\/p>\n\n\n\n

\"Image\"\/<\/figure>\n\n\n\n

In this equation, and are the specific heat capacities of the liquid and vapor form of the substance, respectively, and \u0394Hv<\/sub><\/em> is the latent heat of vaporization at the temperature Tb<\/sub><\/em>. If the phase change involves melting\/fusion or sublimation\/condensation, then the corresponding latent heat value must be used.<\/p>\n\n\n\n

If\u00a0T<\/em>1<\/sub>\u00a0is chosen as 298.15 K\u2014that is, the standard state temperature\u2014then the specific enthalpy of a substance can be calculated at any temperature using\u00a0equation 7.11.<\/p>\n\n\n\n

\"Image\"\/<\/figure>\n\n\n\n

Here, \u0394h<\/em>\u00a0is calculated using\u00a0equation 7.9\u00a0or 7.10, with the lower and upper temperature limits of integration being 298.15 and\u00a0T<\/em>\u00a0K, respectively. The specific enthalpy at 298.15 K,\u00a0h<\/em>298.15<\/sub>, is equal to the standard enthalpy of formation,\"Image\", as previously discussed.\u00a0Equation 7.11\u00a0allows us to compute the specific enthalpy of any substance at any temperature, provided the information on the standard enthalpy of formation and the dependence of the specific heat capacity on temperature are known.<\/p>\n\n\n\n

7.1.4 Enthalpy Changes in Processes<\/h4>\n\n\n\n

The previous discussion should make it clear that it is possible to obtain the values of specific enthalpy of any substance at any temperature. It follows that if a process is carried out at a certain temperature\u2014that is, both the feed and product streams are at that specified temperature\u2014then a certain enthalpy change is associated with that process. The following generic reaction is an example:<\/p>\n\n\n\n

A + (b<\/em>\/a<\/em>) B \u2192 (c<\/em>\/a<\/em>) C + (d<\/em>\/a<\/em>) D<\/p>\n\n\n\n

The enthalpy of reaction (or heat of reaction) is simply the difference between the enthalpies of products and enthalpies of reactants. The following shows this mathematically:<\/p>\n\n\n\n

\"Image\"\/<\/figure>\n\n\n\n

Here, v<\/em> represents the stoichiometric coefficients of the species involved in the reaction. It should be noted that the equation for the reaction is written such that the stoichiometric coefficients of all the other species are normalized with respect to the stoichiometric coefficient of A; that is, the equation involves 1 mole of A and proportional moles of other species. Thus the enthalpy or heat of reaction, \u0394Hrxn<\/sub><\/em> is based on 1 mole of reactant A. Of course, the equation can be normalized on the basis of the stoichiometric coefficient of any other species involved in the reaction, with the enthalpy of the reaction changing proportionately.<\/p>\n\n\n\n

If the process is conducted at standard conditions, then the enthalpy change is termed as the standard enthalpy change<\/em>. For the reaction shown previously, the standard enthalpy of reaction follows:<\/p>\n\n\n\n

\"Image\"\/<\/figure>\n\n\n\n

If the standard enthalpies of the reactants are higher than those of the products, then the enthalpy of the reaction will be negative. The process involves starting with a material having higher chemical energy and ending up with a material with a lower energy. The difference between the two energies (or enthalpies) appears as the heat evolves during the transformation, making the process\u00a0exothermic<\/em>. Conversely, if standard enthalpies of the products are higher than those of the reactants, then the process involves starting with a material of lower energy and ending up with a material having higher energy. Such processes are termed\u00a0endothermic<\/em>.\u00a0Figure 7.2\u00a0shows a conceptual schematic of the enthalpy changes in these two types of processes.<\/p>\n\n\n\n

\"Image\"\/<\/figure>\n\n\n\n

<\/a>Figure 7.2<\/strong> Conceptual schematic of enthalpy changes in endothermic and exothermic processes.<\/p>\n\n\n\n

It is obvious that for an exothermic process, a mechanism for removing heat is necessary if it is desired to maintain a constant temperature. However, if the process is conducted adiabatically\u2014that is, the system does not exchange heat with the surroundings\u2014then the products will be at a higher temperature than the reactants. Conversely, if the process is endothermic, it will require heat input to maintain a constant temperature, and the adiabatic endothermic process will experience a decrease in temperature.\u00a0Figure 7.3\u00a0shows the changes in temperature for an adiabatic system for both endothermic and exothermic processes.<\/p>\n\n\n\n

\"Image\"\/<\/figure>\n\n\n\n

<\/a>Figure 7.3<\/strong> Heat effects in transformations: temperature of adiabatic systems.<\/p>\n\n\n\n

When the transformation involves a chemical reaction, the enthalpy effect is termed the enthalpy of reaction<\/em> or the heat of reaction<\/em>. The enthalpy (or heat) of reaction is termed enthalpy (or heat) of combustion<\/em> when the reaction is of combustion of a substance. Transformations that are physical in nature\u2014that is, transformations that do not involve chemical reactions\u2014are also frequently (usually) accompanied by an enthalpy change. For example, heat effects accompany dissolution of a solute in a solution, and the change in enthalpy is termed enthalpy of solution<\/em> or heat of solution<\/em>. Similarly, enthalpy of mixing<\/em> refers to the enthalpy change when the process involves mixing of different streams. These transformations can be endothermic or exothermic as well. In all these cases, the discussion presented above for reactive systems can be extended, mutatis mutandis<\/em>, to other processes and transformations.<\/p>\n","protected":false},"excerpt":{"rendered":"

Enthalpy is a measure of the energy (or heat) content of a substance [3]. It is a thermodynamic quantity whose\u00a0absolute\u00a0value cannot be determined; however, enthalpy of a substance with respect to its value at some reference conditions can be calculated [4,\u00a05]. The reference state, also called the\u00a0standard state,\u00a0is\u00a0specified in terms of pressure and temperature of […]<\/p>\n","protected":false},"author":1,"featured_media":4601,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[563],"tags":[],"class_list":["post-4671","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-energy-balance-computations"],"jetpack_featured_media_url":"https:\/\/workhouse.sweetdishy.com\/wp-content\/uploads\/2024\/09\/zero.png","_links":{"self":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/4671","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=4671"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/4671\/revisions"}],"predecessor-version":[{"id":4672,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/4671\/revisions\/4672"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media\/4601"}],"wp:attachment":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media?parent=4671"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=4671"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=4671"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}