Q$.2(6$ points$)$

A thermocouple junction may be approximated as a sphere of diameter $2$ mm with thermal conductivity $30\frac{W}{m}.K,$ density $8600k\frac{g}{m^3}$ and specific heat $0\mathrm{.}4k\frac{J}{k}g.K.$ The heat transfer coefficient between the gas stream and the junction is $280\frac{W}{m^2}.K.$ How long $($in seconds$)$ will it take for the thermocouple to record $98$ percent of the applied temperature difference?

$ln(\frac{T(t)-T_{}}{T_i-T_{}})=-\frac{h{A}_s}{V{c}_p}t$