Relative on Volume and Temperature of a adiabatic flow: how can I derive?

The situation is then: In an Adiabatic Flow $(pV^{gamma} = k in mathbb{R})$ we have an fluid element which is decelerated from a velocity $v$ and a region of a pressure $p_{0}$ to the rest and to the region of a stagnation pressure $p_{stag}$. So it makes sense that we want to know what happens if certain physical parameters.

The first fact is, the (relative) pressure variation was given by:

$$frac{Delta p}{p_{0}} = frac{rho v^2}{2p_{0}} = frac{gamma M^2}{2} tag{1}$$

Where, $gamma = frac{C_{T}}{C_{P}}$ and $M$ is the Mach number.

Now, as pressure, we can ask ourselves about the (relative) volume change, $frac{Delta V}{V}$, and (relative) temperature change, $frac{Delta T}{T}$, of this flud element on situation described above.

So my doubt is how can I find the quantities: $frac{Delta V}{V}$ and $frac{Delta T}{T}$ knowing $(1)$ and adiabatic considerations $(pV^{gamma} = k in mathbb{R})$ ?

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Disclaimer: I don’t want a solution properly, just tips on the right way to discover the answer. Also I appreciate references where I can find the route to solution.