# 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

+U

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 E_{2} = E_{1} that is energy of an isolated

system remains constant.