Zeroth and First Law of Thermodynamics

 

Zeroth Law of Thermodynamics

Zeroth law of thermodynamics is also referred to as the law of thermal equilibrium. It was formulated after the enunciation of the first and the second laws of thermodynamics. But it was considered to be of primary importance so it was placed before the first law of thermodynamics, hence the usual name zeroth law. The law, like other laws of thermodynamics is based on experience. The law states that two systems A and B which are in thermal equilibrium with the third system C, are in thermal equilibrium with each other and will have the same temperature. The temperature concept can be stated as - systems in thermal equilibrium with each other have the same temperature and Systems not in thermal equilibrium with each other have different temperatures. The zeroth law therefore provides operational definition of temperature.

The first law of thermodynamics

In the forties of the last century it came to be generally believed that heat was a form of energy and heat and work are interchangeable. Mayer, a German physician, was probably the first to announce in an obscure journal that there is a quantitative relation between the two forms, heat and work, when interchange to takes place. From some crudely arrange experiments in those early days, he could even suggest an astonishingly accurate value of the equivalence between the two forms of energy.

Meanwhile Joule had carried out very thorough and elaborate investigations of this problem and clearly demonstrated from his experiments that the same quantity of heat would always be produced by the performance of a given amount of work, irrespective of the nature of the process in which the work is performed or the substance used in the performance. In other words, there is a strict quantitative relation between the work spent and the heat produced. Hence, if

x calories of heat = y ergs of work

nx calories of heat = ny ergs of work

There is a constant proportionality between heat and work. So,

W = JQ

Where J is the constant of proportionality between the work performed W and heat produced Q. The amount of work required to produce unit quantity of heat and is called mechanical equivalent of heat, denoted by J.

Joule, in his experiments, carried out the performance of work in divers ways. The work was done by

(a) agitating paddle wheels in a mass of water or mercury,

(b) rubbing iron rings under mercury,

(c) passing electricity through a wire known resistance,

(d) compressing air in narrow tubes.

The heat produced was measured from the specific heats of the materials used and the rise of temperature due to friction or passage of electricity. Later on, many other workers carried on the determination of the value of J with considerable accuracy among which the experiments of Rowland, Callendar and Barnes, Laby and Hercules, are especially notable. The accepted value of J is 4.1858 × 10⁷ ergs per calorie.

The relation between heat and work is the origin of first law of thermodynamics which is also known as the law of conservation of energy. The law has been stated in various forms, but the fundamental implication is that although energy may be transformed from one form into another, it can neither be created nor destroyed. In other words, whenever energy of a particular form disappears and exactly equivalent amount of another form must be produced. The first law rules out the possibility of constructing a perpetual motion machine of the first kind - a machine operating in cycles and producing work without any expenditure of energy on it. According to the first law, the total energy of a system and its surroundings, i.e., the universe is conserved. Gain or loss of energy by the system is exactly compensated by the loss organ in energy of the surroundings. The law is universal valid for all processes. In reactions between atomic nuclei, the change in energy is always accompanied by the corresponding change of mass. In this cases the total energy and mass of the isolated system is conserved.

Mathematical formulation of first law of thermodynamics

Consider a system in state A with internal energy E_A. It absorbs from the surroundings a certain amount of heat q and undergoes a change in its state to B where its energy is E_B. This change may be physical, chemical or mechanical. In this scenario the system performs work -W. The energy before change: E_A + q

The energy after change: E_B + (-W)

Therefore the increase in energy of the system ΔE is given by

E_A + q = E_B - W

q = (E_B - E_A) + (-W)

q = ΔE + (-W)

In case of infinitesimal change

dq = dE – dW

When the work is purely P-V mechanical work-

dW = -P_extdV

If P_ext = P (Pressure of the system)

dq = dE + PdV

These are the mathematical forms of the first law of thermodynamics. The heat absorbed is equal to increase in energy of the system plus the work done by the system. If the system loses heat to the surroundings, its energy decreases, ΔE would be negative and work will be done on the system by the surroundings.

The above change can be brought about by a large number of paths. Since E is a state function, its magnitude depends only on the state of the system, the change ΔE will be independent of the path followed. However, the quantities q and W, are path functions, adjust themselves in such a manner that q + W is always equal to ΔE.

Energy change in an isolated system:

If the transformation is carried out under adiabatic conditions such that heat neither enters nor leaves the system. Then dq = 0 and therefore

Therefore from dq = dE - dW, we get

dE = dW

Or dE = PdV

In this case, the work done by the system would be at the cost of internal energy and is equal to the decrease in its energy content. Also, this expression also implies that dW will be exact differential or W will be state function because dE is exact differential and E is a state function.

Energy change in a cyclic process:

If the system after undergoing a change in its state is brought back to its initial state then,

dE = 0

So from the mathematical formula of first law of thermodynamics we get

dq = -dW

q = -W

The heat absorbed by the system from the surroundings is exactly equal to the work done by the system on the surroundings. This expression establishes the impossibility of a perpetual motion of the first kind, i.e., work cannot be produced without withdrawing heat from an external source.

Energy change in a non-isolated system:

Such a system permits the heat exchange with the surroundings. If the system absorbs heat q and performs work, the increase in energy of the system is given by

dE = q + W

The surroundings loses this heat and receives W units of work, the energy change of the surroundings dE* is

dE* = q + W

dE = dE*

The gain in energy of the system is equal to the loss in energy of the surroundings the energy of the system plus the energy of the surroundings is conserved in any transformation.

Reference

1) Peter Atkins, Julio de Paula, Atkins’ physical chemistry book, eighth edition.