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
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