$($Question $4)$

A metallic resistance thermometer has a linear variation of resistance with temperature as $.$ The resistance at $T_0=280K+-0\mathrm{.}01K$ is $R_0=20k+-0\mathrm{.}1\%,$ while at a temperature $T$ the resistance $R$ is $R=30k+-0\mathrm{.}1\%.$ The coefficient ${}_0=\frac{0\mathrm{.}00392}{K}.$

$1-$ Write an explicit expression of $T$

$2-$ Calculate the nominal value of $T$ and its uncertainty.