First Law of Thermodynamics
Category : NEET
First Law of Thermodynamics
First law of thermodynamics was proposed by Helmholtz and Robert Mayer. This law is also known as law of conservation of energy. It states that,
“Energy can neither be created nor destroyed although it can be converted from one form into another.”
(1) Justification for the law : The first law of thermodynamics has no theoretical proof. This law is based on human experience and has not yet been violated. The following observations justify the validity of this law
(i) The total energy of an isolated system remains constant although it can undergo a change from one form to another.
(ii) It is not possible to construct a perpetual machine which can do work without the expenditure of energy, If the law were not true, it would have been possible to construct such a machine.
(iii) James Joule (1850) conducted a large number of experiments regarding the conversion of work into heat energy. He concluded that for every 4.183 joule of work done on the system, one calorie of heat is produced. He also pointed out that the same amount of work done always produces same amount of heat irrespective of how the work is done.
(iv) Energy is conserved in chemical reactions also. For example, the electrical energy equivalent to 286.4 kJ mol-1 of energy is consumed when one mole of water decomposes into gaseous hydrogen and oxygen. On the other hand, the same amount of energy in the form of heat is liberated when one mole of liquid water is produced from gases hydrogen and oxygen.
\[{{H}_{2}}O(l)+286.4\,kJ\xrightarrow{{}}{{H}_{2}}(g)+\frac{1}{2}{{O}_{2}}(g)\];\[{{H}_{2}}(g)+\frac{1}{2}{{O}_{2}}(g)\xrightarrow{{}}{{H}_{2}}O(l)+286.4\,kJ\]
These examples justify that energy is always conserved though it may change its form.
(2) Mathematical expression for the law : The internal energy of a system can be changed in two ways
(i) By allowing heat to flow into the system or out of the system.
(ii) By doing work on the system or by the system.
Let us consider a system whose internal energy is \[{{E}_{1}}\]. Now, if the system absorbs q amount of heat, then the internal energy of the system increases and becomes \[{{E}_{1}}+q\].
If work \[(w)\]is done on the system, then its internal energy further increases and becomes \[{{E}_{2}}\]. Thus,
\[{{E}_{2}}={{E}_{1}}+q+w\] or \[{{E}_{2}}-{{E}_{1}}=q+w\] or \[\Delta E\,=q+w\]
i.e. \[(Change\,in\,internal\,energy)\]=\[(Heat\,added\,to\,the\,system)+(Work\,done\,on\,the\,system)\]
If a system does work (w) on the surroundings, its internal energy decreases. In this case, work is taken as negative (–w). Now, q is the amount of heat added to the system and w is the work done by the system, then change in internal energy becomes, \[\Delta E=q+(-w)=q-w\]
i.e. \[(Change\,in\,internal\,energy)\]=\[(Heat\,added\,to\,the\,system)-(Work\,done\,by\,the\,system)\]
The relationship between internal energy, work and heat is a mathematical statement of first law of thermodynamics.
(3) Some useful conclusions drawn from the law : \[\Delta E=q+w\]
(i) When a system undergoes a change \[\Delta E=0\], i.e., there is no increase or decrease in the internal energy of the system, the first law of thermodynamics reduces to
\[0=q+w\] or \[q=-w\]
(heat absorbed from surroundings = work done by the system)
or \[w=-q\]
(heat given to surroundings = work done on the system)
(ii) If no work is done, \[w=0\] and the first law reduces to
\[\Delta E=q\]
i.e. increase in internal energy of the system is equal to the heat absorbed by the system or decrease in internal energy of the system is equal to heat lost by the system.
(iii) If there is no exchange of heat between the system and surroundings, \[q=0\], the first law reduces to
\[\Delta E=w\]
It shows if work is done on the system, its internal energy will increase or if work is done by the system its internal energy will decrease. This occurs in an adiabatic process.
(iv) In case of gaseous system, if a gas expands against the constant external pressure P, let the volume change be \[\Delta V\] .The mechanical work done by the gas is equal to \[-P\times \Delta V\].
Substituting this value in \[\Delta E=q+w\]; \[\Delta E=q-P\Delta V\]
When, \[\Delta V=0\], \[\Delta E=q\] or \[{{q}_{v}}\]
The symbol \[{{q}_{v}}\] indicates the heat change at constant volume.
(4) Limitations of the law: The first law of thermodynamics states that when one form of energy disappears, an equivalent amount of another form of energy is produced. But it is silent about the extent to which such conversion can take place. The first law of thermodynamics has some other limitations also.
(i) It puts no restriction on the direction of flow of heat. But, heat flows spontaneously from a higher to a lower temperature.
(ii) It does not tell whether a specified change can occur spontaneously or not.
(iii) It does not tell that heat energy cannot be completely converted into an equivalent amount of work without producing some changes elsewhere.
Hess Law
(1) Levoisier and Laplace law : According to this law enthalpy of decomposition of a compound is numerically equal to the enthalpy of formation of that compound with opposite sign, For example,
\[C(s)+{{O}_{2}}\to C{{O}_{2}}(g);\Delta H=-94.3\,kcal\]; \[C{{O}_{2}}(g)\to C(s)+{{O}_{2}}(g);\,\Delta H=+94.3kcal\]
(2) Hess's law (the law of constant heat summation) : This law was presented by Hess in 1840. According to this law “If a chemical reaction can be made to take place in a number of ways in one or in several steps, the total enthalpy change (total heat change) is always the same, i.e. the total enthalpy change is independent of intermediate steps involved in the change.” The enthalpy change of a chemical reaction depends on the initial and final stages only. Let a substance A be changed in three steps to D with enthalpy change from A to B, \[\Delta {{H}_{1}}\] calorie, from B to \[C,\,\Delta {{H}_{2}}\] calorie and from C to \[D,\,\Delta {{H}_{3}}\] calorie. Total enthalpy change from A to D will be equal to the sum of enthalpies involved in various steps,
Total enthalpy change \[\Delta {{H}_{\text{steps}}}=\Delta {{H}_{1}}+\Delta {{H}_{2}}+\Delta {{H}_{3}}\]
Now if D is directly converted into A, let the enthalpy change be \[\Delta {{H}_{\text{direct}}}.\] According to Hess's law \[\Delta {{H}_{\text{steps}}}+\Delta {{H}_{\text{direct}}}=0,\] i.e. \[\Delta {{H}_{\text{steps}}}\] must be equal to \[\Delta {{H}_{\text{direct}}}\] numerically but with opposite sign. In case it is not so, say \[\Delta {{H}_{\text{steps}}}\](which is negative) is more that \[\Delta {{H}_{\text{direct}}}\](which is positive), then in one cycle, some energy will be created which is not possible on the basis of first law of thermodynamics. Thus, \[\Delta {{H}_{\text{steps}}}\] must be equal to \[\Delta {{H}_{\text{direct}}}\] numerically.
(i) Experimental verification of Hess's law
(a) Formation of carbon dioxide from carbon
First method : carbon is directly converted into \[C{{O}_{2}}(g).\]
\[C(s)+{{O}_{2}}(g)=C{{O}_{2}}(g);\,\,\Delta H=-94.0\,kcal\]
Second method : Carbon is first converted into \[CO(g)\] and then \[CO(g)\] into \[C{{O}_{2}}(g)\], i.e. conversion has been carried in two steps,
\[C(s)+\frac{1}{2}{{O}_{2}}=CO(g)\] ; \[\Delta H=-26.0\,kcal\]
\[CO(g)+\frac{1}{2}{{O}_{2}}=C{{O}_{2}}(g);\] \[\Delta H=-\,68.0\,kcal\]
Total enthalpy change \[C(s)\] to \[C{{O}_{2}}(g);\] \[\Delta H=-94.0\,kcal\]
(b) Formation of ammonium chloride from ammonia and hydrochloric acid:
First method : \[N{{H}_{3}}(g)+HCl=N{{H}_{4}}Cl(g);\]\[\Delta H=-\,42.2\,kcal\]
NH4Cl(g)+aq= NH4Cl(aq); DH = + 4.0 kcal
\[N{{H}_{3}}(g)+HCl(g)+aq=N{{H}_{4}}Cl(aq);\] \[\Delta H=-38.2\,kcal\]
Second method : \[N{{H}_{3}}(g)+aq=N{{H}_{3}}(aq);\]\[\Delta H=-8.4\,kcal\]
\[HCl(g)+aq=HCl(aq);\]DH \[=-17.3\,kcal\]
\[N{{H}_{3}}(aq)+HCl(aq)\,=N{{H}_{4}}Cl(aq);\] \[\Delta H=-12.3\,kcal\]
\[N{{H}_{3}}(g)+HCl(g)+aq=N{{H}_{4}}Cl(aq);\] \[\Delta H=-38.0\,kcal\]
Conclusions
(ii) Applications of Hess's law
(a) For the determination of enthalpies of formation of those compounds which cannot be prepared directly from the elements easily using enthalpies of combustion of compounds.
(b) For the determination of enthalpies of extremely slow reactions.
(c) For the determination of enthalpies of transformation of one allotropic form into another.
(d) For the determination of bond energies.
\[\Delta {{H}_{\text{reaction }}}=\Sigma \]Bond energies of reactants – \[\Sigma \]Bond energies of products.
(e) For the determination of resonance energy.
(f) For the determination of lattice energy.
You need to login to perform this action.
You will be redirected in
3 sec
