HERMODYNAMIS reared by Sibarasad Maity Asst. rof. in hemistry For any queries contact at 943445393 he word thermo-dynamic, used first by illiam homson (later Lord Kelvin), has Greek origin, and is translated as the combination of therme: heat, and dynamis: ower. hermodynamics: the science that deals with heat and work and those roerties of matter that relate to heat and work. ERMS AND DEFINIIONS: hermodynamics is the study of the exchange of heat, energy and work between a system and its surroundings. System is the art of hysical universe of interest (Reaction vessel, etc.). he system is enclosed by a boundary (interface searating system and surroundings) which searates it from rest of the universe. Surrounding is the rest of universe (outside the boundary of the system). Boundary wall is of two tyes. i) Diathermal wall which ermits the transmission of heat through it. ii) Adiabatic wall which does not allow any transmission of heat through it. yes of systems: Isolated systems: Systems which are incaable of exchange it s mass and energy with the surrounding. hese have walls or boundaries (adiabatic) that are rigid, do not ermit transfer of mechanical energy, and erfectly insulating and imermeable. hey have a constant energy and mass content. he universe is an examle of an isolated system. losed systems: System which can exchange energy but not mass with the surrounding. It has wall (diathermal) that allow transfer of energy in or out of the system but are imermeable to matter. hey contain a fixed mass and comosition, but variable energy. hese are usually encountered in the laboratory.
Oen Systems: System which can exchange both mass and energy with the surrounding. hese have walls that allow transfer of both energy and matter to and from the system. hese are imortant to engineers in flow systems. Simle Systems: ontain no interior walls. omosite system: wo or more simle systems, and thus contain internal walls. roerties of a system: Exerimentally measurable hysical characteristics which enable us to define or describe the condition of the system are called thermodynamic arameter or roerties of the system. roerties are of two tyes i) Extensive roerties: which are deendent on mass of the system, as for examle volume, surface area, any form of energy(internal energy, enthaly, entroy, Helmholtz free energy and Gibbs free energy), force, and mass etc. If we double the size of the system, then the value of each extensive roerty would also double. ii) Intensive roerties: hich are indeendent of mass of the system, e.g. temerature, ressure, density, refractive index etc. If we double the size of the system, then the value of each intensive roerty will remain unchanged i.e. these are indeendent of size of the system. Exchange takes lace at boundary between system and surroundings during a change in SAE of system. State of a system: State of a system is the set of definite numerical values that are assigned to resective thermodynamic roerties of the system. e.g.(,,) m= kg =5 o =.5m 3 (State-I) m= kg =35 o =.5m 3 (State-II) State»hat condition in which all variables are fixed and unvarying. hen one or more of these variables are changed, the system changes state. Examles: emerature hanges Gas at,, Gas at,, ( = nr is the equation of state for an ideal gas ) hase changes (solid liquid; liquid gas: etc. ) Reactants roducts rocess: rocess means the transformation of a system from one state to another state through a succession of states i.e. change of state. hange of State: imlies one or more roerties of the system have changed. Isothermal rocess: temerature of the system remains constant. Isobaric rocess: ressure of the system remains constant.
Isochoric rocess: volume of the system remains constant. Adiabatic rocess: there is no exchange of energy between system and, the system is insulated from its surroundings State Functions (State ariables) surrounding, that is he state of a system is described by variables known as SAE FNIONS (or FNIONS OF SAE or ROERIES). hese are variables that deend only on the state of the system and not on its history or how the system was brought to its resent state.,, and the thermodynamic functions E or (internal energy), H (enthaly), S (entroy) and G (Gibbs free energy) are state functions. State functions characterize the state of the system, and have the roerty that changes in the function are indeendent of the means by which the change was roduced. It is a remarkable exerimental result that the state of a simle system can be comletely described by secification of just two roerties of the system and the number of moles of each comonent. herefore, in rincile, any one roerty of the system can be determined from two other roerties and the mole numbers. hat is, any roerty is a function of two others and the mole numbers as indeendent variables. he choice of the two roerties is made on the basis of convenience. he following are considered natural variables for the articular roerty (we will see later why this is so): = f(,, n, n n i ) H = f(s,, n, n,..n i ) E = f(s,, n, n,..n i ) S = f(e,, n, n,..n i ) G = f(,, n, n,..n i ) he first equation is called an equation of state that relates, and. For a gas the equation is = nr/. he other equations are known as fundamental equations and rovide comlete knowledge for comuting equilibrium conditions of a system. Of course we would need a real functional relationshi to do this. e will obtain the functional form for E and G later. State function versus ath function: A state function is a function that deends only the current roerties of the system and not on the history of the system. e.g. density, temerature, and ressure. A ath function is a function that deends on the history of the system. e.g. work and heat. hermodynamic state sace. Since the number of variables needed to secify a roerty is only for a fixed comosition, we can visualize equilibrium states on a simle lot of 3 dimensions (if comosition were a variable, we would need more dimensions). Because any roerty deends only on the resent state of the system, and not on how it was created, changes in state functions do not deend on the ath taken, i.e., for either ath shown from state to state : 3
State:(,, ) State-(,, ) Δ =, Δ =, Δ = Microscoic and Macroscoic Aroach: o study the behavior (changes in & ) of substances we have aroaches Microscoic Aroach: Study behavior of each atom & molecule (Quantum mechanics) Macroscoic Aroach: Study average behavior of many atom & molecule. a) Find the average behavior based on robability theory (Statistical thermodynamics) b) Find the average behavior using instruments. hermodynamics deals with macroscoic observable roerties of matter. e study the average behavior of many atoms/molecules using instruments. e.g. average ressure (using a ressure measuring device) average temerature (using a thermometer). Heat: In thermodynamics heat is defined as a quantity that flows across the boundary of the system during change in its state by virtue of difference in temerature between system and it s surrounding and flows from a oint of higher to lower temerature. ork: ork is defined as quantity that flows across the boundary of the system during change in its state and is comletely convertible into the lifting of a weight in the surroundings. hat means work is done if the rocess can be used to bring about a change in the height of a weight somewhere in the surroundings. Energy is the caacity to do work. alculation of work: e begin by discussing mechanical work and aim at getting exressions for dw. Mechanical work includes the work required to comress gases and the work that gases do when they exand. Many chemical reactions involve the generation of or the reaction of gases, and the extent of reaction deends on the work the system is allowed to do. he sign convention: dw is ositive it signifies that work has been done on the system. dw is negative it signifies that work has been done by the system on the outside world. hen an object is dislaced along a ath through a distance dz against a force F(z) the amount of work that has to be done on it, is 4
dw = F(z)dz. [ork = force dislacement] he force (F(z)) has a sign: if it ushes towards +Z (oosing motion downwards), it is ositive; if it ushes towards Z (oosing motion uwards), it is negative. he work sent (w) in moving the object from z i to z f is the sum of the work required to move it through all the segments dz of the ath.i.e. z f w F( z) dz zi Exansion work by gases: If a system alters its volume against an oosing ressure, a work effect is roduced in the surrounding. his exansion work aears in most ractical situations. Here the system is a quantity of a gas contained in a cylinder fitted with a iston which is frictionless and weightless. he cylinder is immersed into a thermostat so that the temerature () of the system is constant throughout the change in state. In the initial state-i(, ) when there is two bricks having weight M and m resting on the iston no movement of iston was found i.e. there is the equilibrium in the system and ressure of the gas is equal to the ressure imosed by those two bricks of mass M and m. If we remove the mass m from the iston, the equilibrium will be disturbed and ressure of the gas will now become more than the ressure imosed by the brick of mass M only. Now the iston will rise until unless ressure of the gas will become equal to the ressure due to mass M on the iston and new equilibrium is reached, state-ii (, ). During this rocess the gas exands from volume to and ressure changes from to.ork is roduced in this transformation since mass M has been lifted vertically by distance h against the force of gravity Mg. he quantity of work roduced is = Mgh If the area of the iston is A, then the downward ressure acting on the iston is Mg/A= o or ext, the ressure which ooses the motion of the iston. hus = Mgh = o Ah 5
However, the roduct Ah is simly the additional volume enclosed by the boundary in the change of state. hus, Ah= - and we have = o ( - ) Exansion work: w = ( ext A)h = ext Δ Modern Sign onvention: Having a - sign here imlies w > if Δ <, that is, ositive work means that the surroundings do work to the system. If the system does work on the surroundings (Δ >) then w <. Multistage Exansion: In a multistage exansion from state (, ) to state (, ) the work roduced is the sum of the small amounts of work roduced in each stage. If o is constant as the volume increases by an infinitesimal amount d then the small quantity of work d is given by d= o d otal work roduced in the exansion from to is the d o d his is the general exression for the work of exansion of any system. Once o is known as a function of the volume, the integral is evaluated as usual methods. omression work: omression work is comuted using the same equation that is used to comute exansion work. But in comression the final volume is always less than the initial volume so in every stage is negative. w ork is ath deendent function: let s check this!! Let us consider a quantity of gas in a cylinder fitted with a iston on which three bricks of weight 3, and unit (say kg) are laced. At that condition there is the equilibrium, means there is no movement of the iston, say this is the initial state (, ). hat means the ressure equivalent to three bricks of weight 3, and unit (say kg) laced on the iston of the cylinder, as shown in figure:. It is now allowed to exand isothermally until unless its state becomes (, ). ase-i: e can change the state directly from (, ) to (, ) through exansion as shown in figure: by removal of the brick of weight 3 unit. By this way we can reach the state at (, ) where the ressure is equivalent to two bricks of weight and unit. If we look into the rocess attentively the exansion occurs against the constant ressure of [ + ] unit. So o = and the exansion work is o d 6
w d o d = o ( ) = ( ) If we lot versus at constant temerature we can trace the area which can signify the magnitude of as shown by the area ABD in figure:a. ase-ii: In other way if we can change the state from (, ) to (, ) in two ste rocess via state ( ', '), as shown in figure: by the removal of one brick of weight unit in st ste followed by removal of the brick of weight unit in nd ste. In ste: exansion occurs against a constant ressure due to two bricks of weight (3+) unit which is equivalent to ressure ' and in nd ste exansion occurs against a constant ressure due to bricks of weight (3) unit which is equivalent to ressure. So the work done by the system in ste: is S = '( '- ) And the work done by the system in ste: is S = ( - ') As shown in figure:b ; area AEFG and area BEH signify the quantity of work S and S resectively. So the total work in two ste exansion from (, ) to (, ) via state ( ', ') is the sum of the area AEFG and BEH. If we comare the case-i and case-ii; from grahical view it is clear that in two stage exansion more work is done by amount DHFG comare to single stage exansion. So we can conclude that exansion work should be roduced more and more with increase in number of stes of exansion keeing the initial state ((, ) and final state (, ) exactly same. For multistage exansion we can exect maximum exansion work to be roduced. hat means the function work not only deends on the initial and final state but also the way (ath) of change of states so work is ath deendent function. 7
So far we have seen how the quantity of exansion work increases with increase in number of stage of exansion. Let us now check what haens if we comress the gas from state (, ) to (, ), just reverse way to the exansion rocess we discussed earlier. ase-iii: If we can carry out the comression in one stage (, ) to (, ) by returning the brick of weight 3 unit as shown in figure:. Amount of comression work ( ) that is to be done on the system is o d he quantity of comression work is described by the area ABIJ, as shown in figure: a ase-i: If we comress the gas in two stage from state (, ) to (, ) via ( ', ') by returning the bricks of weight and unit resectively on the iston; the work done on the system in each stage will be as following. he work done on the system in comression ste: is: - = '( '- ) And the work done on the system in comression ste: is: - = ( - ') So total comression work = - + - = '( '- )+ ( - ') 8
As shown in figure:b ;area BEFL and area AEKJ signify the quantity of work - and - resectively. So the total work done in two ste comression from (, ) to (, ) via state ( ', ') is the sum of the area BEFL and area AEKJ which is clearly less than the area ABIJ as shown in figure:a. hat means with increase in number of stage of comression the amount of work that is to be done on the system gradually decreases. How can we get maximum work? From the above calculation done in ase-i, II, III, and I we learnt that with increase in number of stage, amount of exansion work done by the system gradually increases whereas amount of comression work that is to be done on the system gradually decreases i.e. to get maximum work we will have to execute multi ste exansion and comression. o have this multi ste rocess let us lace a sand bag of weight (m ) and remove the sand article one by one for exansion and return those sand article one by one for comression. During exansion the ressure dro in each ste of exansion by very little d amount. If we assume that the initial ressure of the gas is balanced by mass (of sand bag) m, then exansion will take lace if the external(or oosing) ressure o (due to weight of sand bag which varies with exansion) is just d amount less (due to removal of one sand article) than the internal ressure(say, int ) at each stage of exansion and it is true for each stage of exansion. So mathematically we can calculate the total work done ( multiste ) by the system for state change from (, ) to (, ) through multi stage exansion as- multiste o d int d d int d dd int d It is seemed o = int for multistage (infinite ste) exansion, neglecting the term ddv which is infinitesimal of higher order than the first term and so has a limit of zero. So the general exression for maximum work in exansion: max int d an 9
Similarly, we find the minimum work required for comression from (, ) to (, ) by setting the value of o at each stage jus infinitesimally greater than the ressure of the gas; o = int +d. he argument will obviously yield the following equation. Exression for minimum work in comression: For the ideal gas, the maximum quantity of work roduced in the exansion or the minimum destroyed in comression is equal to the shaded area under the isotherm in the following figure:4. min int d Reversible and irreversible rocess: ***** Definition: During any cyclic rocess if system is restored to its initial state but surroundings are not restored to their original state then the rocess is called irreversible. During any cyclic rocess if the system as well as surroundings is restored to their initial state then that rocess is called reversible. Exlanation: Let us consider the same system as before, a quantity of gas in a cylinder at a constant temerature. Exand the gas from (, ) to (, ) as mentioned in case-i and then comress the gas to the original state as discussed in case-iii. he gas has been subjected to a cyclic transformation returning at the end to its initial state. So there is no change in original state of the system. But let us check what haens in surroundings? ork done on the surroundings in the exansion is, ex = ( ) ork done by the surroundings in the comression is, com = ( - ) he net work effect in the cycle is the sum of these two: cy = ex + com = ( ) + ( - ) = ( - ) ( ) = - ve Since ( ) is ositive and ( - ) is negative cy is negative. So the system is restored to its initial state but the original state of surroundings is not restored. So it is the case of irreversible rocess.
On the other hand in case of the multistage exansion and comression as we have discussed earlier (figure:4) net work effect in the cycle is zero as shown below. cy ex com int d int d In this case system as well as surroundings is restored to their initial state so it is the examle of reversible rocess. Reversible rocess Irreversible rocess i. he rocess occurs very slowly. i. he rocess occurs very raidly. ii. he driving force and oosing force differ by ii. he driving force and oosing force differ an infinitesimal amount. widely. iii. Maximum work is obtainable in this rocess. iii. ork obtainable is always less than iv. he changes occurring in the forward rocess reversible rocess. can be reversed exactly in the backward rocess. iv. he changes occurring in the forward rocess v. It involves infinite number of stes. can never be reversed exactly in the backward vi. It is urely concet and can not be realized in rocess. actual ractice. v. It does not involve many stes. vi. Most of the natural rocess as well as man made laboratory synthesis are irreversible. ork in irreversible exansion of gases: If the gas exands against constant external (oosing) ressure of atm; is irreversible exansion and during change in its state from (, ) to (, ) at temerature, the work done may be written as, Irreversible d If the gas is ideal in nature then ork in reversible exansion of gases: o o If n moles of ideal gas exands at temerature (isothermally) against variable ressure then the exansion is reversible in nature and work done during change in its state from (, ) to (, ) is irrev, ideal nr nr nr reversible, iso, ideal int d d nr ln nr ln
For van der aals gas n a nb nr nr nb n a rev, iso, real nr nb n a d nr ln nb nb n a Reversible work is greater than irreversible work: w rev w irrev nr ln nr nr ln nr w rev w irrev nr nr nr ve his is always ositive irresective of the magnitude of and. hus rev is greater than irrev. Internal energy: he energy which a system should ossess because of the motion and configuration of its atoms, molecules and subatomic articles is called internal energy or intrinsic energy. It is denoted as or E. Internal energy is the sum of kinetic energy and otential energy. Kinetic energy is associated with translational, rotational, vibrational, bond energy, electronic and nuclear energy. otential energy is due to interaction with neighbouring constituents. In case of ideal gas there is no intermolecular attraction whereas for real gases there exist mutual forces of attraction between molecules. herefore the molecules of real gases ossess intermolecular otential energy. During exansion of real gas work needs to be erformed by the gas against intermolecular attraction and hence otential energy will change, thus intermolecular otential energy of real gas is function of its volume. According to kinetic theory of gases average kinetic energy of molecules deends on temerature as So internal energy is taken as the function of temerature () and volume (), i.e. for closed system having real gas = f (,) and since ideal gas has no intermolecular otential energy for ideal gas = f () It is a state function and extensive roerty In a change from some Initial State Final State Δ = change in = final - initial and d is also erfect differential, i.e. 3 K. E. k
Question: Show that internal energy is erfect differential? Answer: e know for one mole ideal gas =R R or R Again, R or R hus, d is erfect differential. Again, we have seen that = f() for an ideal gas i.e. and hence d becomes erfect differential. First law of thermodynamics: It is the law of onservation of Energy. he total energy of the universe (or any isolated system) is constant. Energy can neither be created nor destroyed but can be converted from one form to another. Let a system be in state I with internal energy I undergoing a change to state II with internal energy II. During this change of state the system absorbs dq amount of heat from the surroundings also erforms some work (may be mechanical, electrical etc.) then the net energy before transformation = I +dq and net energy after transformation = II + then according to st law of thermodynamics net energy before transformation = net energy after transformation i.e. I +dq = II + or dq = ( II I ) + Or dq = d + his is the mathematical form of st law. For a system erforming mechanical work (exansion or comression of gas) dq = d+ o d he heat change at constant volume Q = Enthaly or heat content: hemical rocesses generally carried out in oen vessels where ressure remains constant, then heat changes in not equal to. In order to deal with thermal effects for rocesses run at constant ressure, a new thermodynamic arameter called enthaly or heat content, denoted as H is introduced. Mathematically it is exressed by the following equation. H = + Since the ressure and volume of a system deends only on its state, the roduct also deends on the state. he function H being a combination of state variables is itself a state function. It is also a erfect differential and extensive roerty. his function signify the energy, stored within the 3
system, that is available for conversion into work. Like internal energy the absolute value of heat content (H) can not be measured, only things which can be measured exerimentally is the change in enthaly ( H). Question: Is H always equal to Q? Answer: By definition we know H = + ; where H is enthaly, is internal energy, is ressure and is volume occuied by the system. hange in enthaly during any rocess, By st law of thermodynamics we have For a system erforming mechanical work only If o =, which is strictly true for reversible system, then H = + + dq = d + dq = d + o d dq = d + d Hence H = + + = Q + At constant ressure, H = Q So H is equal to Q for a system erforming reversible mechanical work only, not always it is true. Measurement of : Joule exeriment: Identification of the differential coefficient with readily measurable quantities is not so easily managed. For gases it can be done, in rincile at least, by an exeriment devised by Joule. Joule carried out exeriment on free exansion. Exansion of gas against zero ressure (vacuum) is called free exansion. wo containers A and B are connected through a stocock. In the initial state the container A is filled with a gas at ressure which is suosed to be very low to bring ideality in the system. he container B is comletely evacuated. he entire assembly (system) is immersed in a large volume of water (surroundings) and is allowed to come in thermal equilibrium with water. he temerature of the water was noted as. he stocock is now oened and the gas is allowed to exand against vacuum ( o = ) till the both containers become uniformly occuied by that gas and then temerature of water is again noted. he result shows that temerature of water before and after exansion remains unchanged. So here no exchange of heat energy between system (two containers with stocock) and surroundings (water) was observed, means the rocess is adiabatic. So dq = he work done by the system through this free exansion = o hange in volume of gas 4
From st law we know dq = d + Or, = d + Or, d = = hange in volume of gas = Hence the rocess is isothermal. So free exansion of ideal gas is isothermal at the same time adiabatic in nature. Now = f (,) hen, the change in energy d can be exressed as, Since, d = and d = e have d but d So, d d d If the derivative of energy with resect to volume is zero, the energy is indeendent of volume. his means the energy of ideal gas is a function of temerature only. Again, But Further, H = + so H Since for ideal gas onsequently, H for ideal gas. ( R) So for ideal gas H H But for real gas there is intermolecular attraction so during free exansion also gas will have to overcome this attraction. Hence internal energy slightly decreases. e will see later that for one mole real gas a 5
Heat caacity: Amount of heat required to raise the temerature of one mole substance through o or K is called heat caacity(). If dq amount of heat is required for d increase in temerature of one mole of the substance then dq d ; but dq is ath function and is value deends on the actual rocess followed. wo aths are there one at constant ressure and other at constant volume. hus dq and d Hence, d d and dq d but we know dq v = d and dq = dh dh d i.e. d = v d and dh = d assuming v and remain unaltered in the temerature range of investigation. In general is greater than v. olume of a substance generally increases at constant ressure with rise in temerature. So art of the heat is utilized to erform extra mechanical work while at constant volume all he heat is utilized in increasing internal energy of the system as there is no work. hat s why is generally greater than v. Relation between and v : e know that for closed system having one mole of the substances = f (,) hen, d d d Hence Again we know, H = +.(i) hen, H So, H sing eq n (i) Or,.(ii) Equation (ii) is the general relation and is valid for any substance like solid, liquid or gas. 6
For solid/liquid so, v For water in the range of o to 4 o ; ve i.e. < v For gases ve so > v For ideal gas = So, For one mole ideal gas = R So, R So, for one mole ideal gas R Adiabatic reversible rocess: An adiabatic rocess is one in which the heat is neither gained nor lost by the system, i.e. dq = From st law of thermodynamics we know dq = d + Hence for adiabatic rocess Again we have d = v d, the = d + = v d +.(i) If only mechanical work (exansion or comression) is involved then If the exansion or comression is reversible in nature then sing equation (i) we get = v d + int d For the system containing one mole ideal gas, herefore, v d + Or, v d + d R d = int d = d Or, R o int = o d d d Or, ( ) where Integrating we get, d Or, ln + ( ) ln = ln Or, onst. d ( ) ln.(ii) 7
Again, for one mole ideal gas = /R So, R cons tant or, onst. R Again,, utting this in onst. we get R onst. or, onst. All these relation are valid for a system containing one mole of ideal gas which undergoes reversible adiabatic exansion or comression. If we change the state of a system containing one mole of ideal gas from (, ) to (, ) through exansion or comression, adiabatically and reversibly then using equation (ii) we can have d ( ) d or, ln ( ) ln or, or, Show reversible adiabatic - curve is steeer than reversible isothermal - curve. For reversible adiabatic exansion of ideal gas K(onst.) So, the sloe of adiabatic - curve d d K (i) For reversible isothermal exansion of ideal gas So, the sloe of isothermal - curve d d = R =K ' (constant) K...(ii) Both the sloes are ve but the sloe of adiabatic is more ve since for gases is greater than one. So the sloe of - curve for adiabatic change is steeer than the corresonding isotherm. 8
Now since the area under - curve is equal to the work done, it is obvious that the work is more in isothermal exansion than in adiabatic exansion for the same volume change. Adiabatic work and isothermal work: From st law of thermodynamics we know Q = + For adiabatic exansion dq =, so = + ad Or, ad = - v = v ( - ) For mole ideal gas, R ad, ideal ad, ideal R R For isothermal change = constant So, d + d = Or, iso,rev = -d For adiabatic change = constant So, d d Or, d d d Or, ad, rev d ISO, RE d So, d AD, RE So isothermal work is greater than adiabatic work. 9
hermochemistry All chemical reactions and few hysical changes are associated with energy change. In most cases this energy is heat energy but there are cases where this may be light or electricity also. hermochemistry deals with energy change associated with chemical changes and their alication. A thermochemical equation is a chemical equation where not only reactants and roducts but also their comlete states (solid, liquid or gas) have to be mentioned.(since the heat quantities deend on the hysical state of matter). (s) + O (g) = O (g) + Q kcal at o and atm. H (g) +/ O (g) = H O(l) + 85.8 kj at 5 o. his reaction normally takes lace in oen vessel so that is constant of atm. he reaction in which heat escaes from the system to the surroundings is termed as exothermic. hile if heat is absorbed by the system from surroundings is endothermic. Heat of reaction: According to old convention heat of reaction is the amount of heat evolved or absorbed during reaction. According to modern convention heat of reaction is the difference in total energy of roducts and reactants. From st law of thermodynamics, dq = d + d At constant volume, Q v = Again H = + so, H = + + At constant ressure, H = Q his means for reactions involving gaseous substances, energy change i.e. heat of reaction in any chemical reaction is related to H rovided the reaction is erformed at constant ressure and it will be the reaction is erformed at constant volume. hus heat of reaction is denoted as H or But in most of the cases reactions are carried out in oen vessels where ressure is constant that s why mostly heat of reaction is denoted as H. It will be denoted as when we carry out a reaction in closed container where volume remains constant. onsidering enthaly as total energy heat of reaction at constant, H H roducts H reac tan ts At constant volume, roducts reac tan ts For exothermic reaction H = -ve and for endothermic reaction H = +ve (s) + O (g) = O (g) H = - 94 kcal N (g) + O (g) = NO(g) H = + 4 kcal H value should be reorted by mentioning and.
Relation between H and : Let us consider a reaction involving gaseous substance r he corresonding state change r (,, ) (,, ' ) e know, H = + and H r = r + So H = H H r = ( r ) + (`-) or, or, n R nr R H H nr Assuming the gases behave ideally. n is the difference in no of moles of gaseous roducts and reactants. hen n=, H = ; If n=-ve H > and if n=+ve H >