$18\mathrm{.}62$ :: $$A light, plastic sphere with mass$$m $=9\mathrm{.}0$ g and density $=4$ kg$/$m$3$ is suspended in air by thread of negligible mass.

$($a$)$ What is the tension, FT$,$ in the thread if the air is at T$0=5$C and p $=1$ atm? The molar mass of air is Mair $=28\mathrm{.}8$ g$/$mol$.$ Be sure to find a solution that is dependent only on the given variables m$,$ $,$Mair $,$p$,$ and$$T$0$ as well as some constants.

$($b$)$ How much does the tension in the thread change if the temperature of the gas is increased to Tf $=35$C$?$ Ignore the change in volume of the plastic sphere when the temperature is changed. Remember to solve symbolically before plugging in any numbers $($and when you do plug in$,$ don$$t forget your units!$)$Hint #$1$: check out what happens to the air's density when the temperature changes. Hint #$2$: do not ignore the buoyancy of the sphere.