In: Chemistry
Prove that Inter energy is Independent of the path
Let the ‘X’ be the initial state of the system and ‘Y’ is the final state of the system. Now let suppose UX and UY are the energies of the system in its state ‘X’ and ‘Y’ respectively. Hence Change in internal energy will be given by:
ΔU = UY – UX
Now let us assume that system
changes from state X to state Y by following Path I and change in
energy is accompanied by ΔU.
Now suppose that by using another path II the same change of state
is brought and energy change associated with this be
ΔU’.
Let, ΔU is greater than ΔU’ i.e.
ΔU> ΔU’
By coupling of these two processes:
X ——-> Y (by path I) and
Y ——-> X (by path II)
It is shown in figure below
The system will come back to its
initial state and at the same time the energy which is used will b
available which is equal to ΔU- ΔU’. Repeating the same
cycle again and again , continuous energy will be generated and
perpetual motion will become possible. This is contradiction to the
first law which states that energy can neither be created nor be
destroyed.
Hence,
ΔU = ΔU’