Next, consider the same initial situation but now with the walls at the same temperature as the gas. When the piston is pushed slowly to compress the gas, the gas molecule collides with the piston coming towards it and the speed of the molecule increases on collision (assuming elastic collision, v2= v1 + 2u in the figure below). This way the internal energy of the molecules increases as the piston is pushed in.
We see that the total internal energy of the gas can increase either due to the temperature difference between the walls and the gas (heat transfer) or due to the motion of the piston (work done on the gas).
In a general situation, both modes of energy transfer may happen together. As an example, consider a gas kept in a cylindrical can, fitted with a movable piston. If the can is kept on a heater, the hot bottom of the cylinder supplies heat to the gas. If the piston is pushed out to some distance, as the piston moves out, the gas does work and the gas loses that amount of energy. Thus, the gas gains energy as heat gets supplied to it and it loses energy as work is done by it.Suppose, in a process, an amount DQ of heat is given to the gas and an amount DW of work is done by it, the total energy of the gas must increase by (DQ - DW). As a result, the entire gas, together with its container, may start moving (systematic motion) or the internal energy (random motion of the molecules) of the gas may increase. If the energy does not appear as a systematic motion of the gas, then this net energy (DQ - DW) must go in the form of its internal energy. If we denote the change in internal energy as DU, we get
Equation (1) is the statement of the first law of thermodynamics. In an ideal monatomic gas, the internal energy of the gas is simply translational kinetic energy of all its molecules. In general, the internal energy may get contributions from the vibrational kinetic energy of molecules, rotational kinetic energy of molecules as well as from the potential energy corresponding to the molecular forces. Equation (1) represents a statement of conservation of energy and is applicable to any system, however complicated it might be.
Spontaneity of processes
The term spontaneity means the feasibility of a process. A process which can take place by itself under the given set of conditions once it has been initiated if necessary, is said to be a spontaneous process. The spontaneous processes are called feasible or probable processes. It may be noted that the term spontaneous should not be taken to mean that the process occurs instantaneously. It simply predicts that the process has an urge to proceed or it is practically feasible. The actual rate of the process may vary from very slow to extremely fast.There are also some processes which require some initiation before they can proceed. But once initiated, they proceed by themselves. These processes are also regarded as spontaneous processes.
Thus, the spontaneous processes may be of two types.
(a) Spontaneous processes where no initiation is needed
(i) Sugar dissolves in water and forms a solution
(ii) Water keeps on evaporating from ponds, rivers, sea and open vessels
(iii) Nitric oxide (NO) and oxygen react to form nitrogen dioxide
b) Spontaneous processes where some initiation is required
(i) Once a reaction between hydrogen and oxygen is initiated by passing electric spark through it, then it occurs itself spontaneously even at room temperature.
(ii) In domestic oven, coal (carbon) keeps on burning once initiated ignition
(iii) Methane burns with oxygen once ignited.
From the above reactions, it can be concluded that the spontaneity (or feasibility) means the inherent tendency of a process to occur of its own in a particular direction under a given set of conditions.On the other hand, the processes which are forbidden and are made to take place only by supplying energy continuously from out side the system are called non-spontaneous processes. For e.g., water can be made to flow up hill (reverse of natural tendency) with the help of a machine. This can continue as long as the external energy is supplied to it. When the supply of energy is cut off, the process stops.
The natural tendency of various processes to occur spontaneously leads to a very curious question in our mind. "What is the driving force which makes a process spontaneous?"
Spontaneity of a process and Enthalpy change
It is a well-known fact that all physical and chemical processes are accompanied by energy changes. It is possible to interpret various spontaneous processes on the basis of changes in energy. Consider the spontaneous processes such as falling of a cricket ball from our hands to the ground; flowing of water from higher level to lower level. It is known that the ball or water possesses more potential energy at higher level than at lower level. This suggests that these spontaneous processes proceed by decrease of energy. Moreover, the state of lowest energy corresponds to the state of maximum stability. Therefore, the natural tendency of all systems in this universe to go from unstability to stability supports the fact that any process which involves a decrease in energy should have an inherent tendency to take place.Most of the spontaneous chemical reactions are also found to be exothermic.
Thus, it may be concluded that all those processes which are accompanied by decrease of energy (exothermic reactions. having negative value of DH) occur spontaneously. In other words, the sign of DH may be taken as a criterion for the spontaneity of a process and decrease of enthalpy or DH may be regarded as the driving force behind the spontaneous processes.
Limitations of criterion of decrease of Enthalpy
The criterion of decrease of enthalpy for the feasibility of chemical reactions fails to explain the following facts:
a) Endothermic reactions are also known to occur spontaneously
There are a number of endothermic reactions (DH, positive), which are known to be spontaneous. A few examples of such processes are given below:i) Evaporation of water is an endothermic process but it is spontaneous in nature.
ii) Dissolution of ammonium chloride in water is endothermic but occurs spontaneously.
iii) Decomposition of mercuric oxide on heating.
b) Reactions do not go to completion
Most of the reactions do not go to completion even though DH remains negative throughout. In fact, all spontaneous chemical reactions proceed only until an equilibrium is attained.
c) Reversible reactions also occur
Most of the reactions are reversible in nature. In these reactions both the forward and the backward reactions occur simultaneously. For e.g., in the following reaction, the forward reaction is exothermic; but the backward reaction is endothermic:
But both the reactions occur. This means that reactions with negative value of DH as well as positive value of DH are occurring simultaneously. It may be concluded that tendency to have minimum energy, -DH, may be the criterion for a process to be spontaneous but it cannot be the only or sole criterion.