$13-(1$ point$)$ A material exhibits a magnetostructural transition between two phases I and II

such that the transition temperature $II$I depends on the stress and on the magnetic field as

$T_{II\text{I}}=320+0,2($at ${}_{0}H=0)$ and $T_{II\text{I}}=320-4{}_{0}H($at $=0),$ respectively $($where $T$ is

in $K,$ in MPa and ${}_{0}H$ in T$).$ These two straight lines determine the planar coexistence

surface of the $3-$dimensional phase diagram $(T--H).$ In turn, the transition $T_{III}$ presents

a hysteresis at constant field of $20K$ which is independent from the fields. If$,$ starting from $330$

$K$ in the absence of the fields, the system performs the following trajectory:

Increase of stress up to $100$MPa $($i$)$ Cooling of $30K($ii$)$ Increase of the magnetic field up

to $2T($iii$)$ Heating of $10K($iv$)$ reduction of the stress down to $50$MPa $($v$)$

in what phase the material will be after each process?