*K*_{T,0} is the isothermal bulk modulus [Wiki] at zero
*P*. Its definition is:

(1)

Then,

(2)

or more strictly,

(2')

By integrating Eq. (3), we have:

(3)

The integral constant *C* is determined from the condition that *V* = *V*_{0} at *P* = 0:

(4)

By substituting Eq. (4) into Eq. (3), we have:

(5)

Eq. (5) is the simplest EOS. However, it is not applicable for our interest, because materials become more incompressive due to compression, or with increasing *P*. Therefore, we need an
EOS in which *K*_{T,0} increases with *P*.

It is noted that, although some literature shows a line for the simplest EOS in the *V*/*V*_{0} - *P* space, it is incorrect, as is seen from Eq. (5). The blue curve
of Fig. 1 (below) shows the *V*/*V*_{0} against *P* by the simplest EOS. Of course, the intersection of the tangential line of the simplest EOS with the *P*
axis shows *K*_{T,0}.

*V*_{0} - P relations by the simplest EOS (blue) and Murnaghan linear EOS (orange). Note that the relation by the simplest EOS is also curved and deviated from the
linear relation. _{}