# First law of Thermodynamics

First law of thermodynamics (law of conservation of energy)

The first law of thermodynamics is simply a statement of the principle of conservation of energy. This law was first enunciated by Julius Robert Mayer (1842) and this great concept was first explained by Helmholtz in 1847. This law states that:

‘The energy of an isolated system remains constant, although it may be changed from one form to the other’. Or Energy can neither be created nor destroyed but can be converted from one form to another form.

Thus the heat supplied to a system is never lost but is partly converted into internal energy and partly in doing work by the system.

In other words, $\therefore$ Heat supplied = Work done by the system + Increase in internal energy $\therefore$ Increase in internal energy = Heat supplied – Work done by the system

This statement can be mathematically represented as:

dE = q – w

Where dE is the increase in internal energy in the system, q is the heat supplied and w is the work done by system.

Explanation: Consider a system represented by a state A in the figure. Suppose the conditions are now altered so that the system moves to B by the path I and then brought back to the state A by a different path II. As a consequence of first law of thermodynamics the total energy change at A is nil. Internal Energy as a function of State

If it is imagined that the energy involved in path I is greater than in the returning path II, then certain amount of energy would have increased in the system on its own  accord. This is against the first law of thermodynamics and so it must be concluded that the net energy change of a system will depend on the initial and final states but not on the path followed. Let E A represents the energy in the state A and EB in the state B, the increase in energy on passing from A to B may be given by: $dE = \Delta E = E_B- E_A$…..(x)

which is independent of the path taken. The quantity is called the internal or intrinsic energy. When a system changes from one state to another it may lose or gain energy as heat and work. Suppose the heat absorbed by a system is Q. If in a change from A to B the energy constant of the system is increased by AE, the work done being W, then according to first law: $\Delta E = Q- W$  …(xi)

The above equation is a form of first law of thermodynamics. Thus the difference between heat absorbed and the total work done by the system is equal to the increase in the energy content.

For infinitesimal change, the above equation may be put as:

dE = dQ – dW

or dE = q – w …..(xii)

where dE is the small increase in energy and q and w represent small quantities of heat absorbed and external work done by the system, respectively.

If as a result of a series of processes the system returns to its original state then its energy content remains unchanged so that $\Delta E$ must be zero. In such a case, it is evident that work done is equal to heat absorbed in the process.

I.e.

q = w ……(xiii)

This equation is an expression of the impossibility of perpetual motion of the first kind i.e. creation of energy out of nothing. This law has following limitations:

(i)    Why heat cannot be completely converted into work.

(ii)   It does not explain the spontaneity of the process.

(iii)   It puts no restriction about direction flow of heat.

Unforgetable Guidelines

‘q’ is positive : If heat is absorbed by the system.

‘q’ is negative : If heat is evolved by the system.

‘w’ is positive:  If work is done on the system.

‘w’ is negative:  If work is done by the system.

For adiabatic process, q = 0, $\therefore w = -\Delta E$

For isothermal and cyclic processes, $\Delta E = 0, \therefore q = w$

For isochoric process, $qv = \Delta E$

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