Energy is a property of the system

Energy is a property of the system

By rearranging
we can have

2b1 (dQ – dW) = ∫2c1 (dQ – dW)

It shows that the integral is the same for the paths 2-b-1 and
2-c-1, connecting the states 2 and

1.   That is, the quantity ∫ (dQ – dW) does not depend on the path
followed by a system, but depends only on the initial and the final states of
the system. That is ∫ (dQ – dW) is an exact differential of a property. This
property is called energy (E). It is given by

dE =  dQ-dW E = KE + PE

where U is the internal
energy. Therefore,

dE = d(KE) + d(PE) + dU = dQ-dW

Quit often in many situations the KE or PE changes are negligible.

dU = dQ – dW

An isolated system does not exchange energy with the
surroundings in the form  of work as  well as heat. Hence dQ = 0 and dW = 0. Then the first law of thermodynamics reduces to dE

= 0 or E2 = E1 that is energy of an isolated
system remains constant.

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