A student assistant uses a cylindrical projectile launcher to throw rubber spheres horizontally at a nearby vertical target. Using a radar gun, she establishes that a sphere with a mass of $0\mathrm{.}150$ kg and diameter of $8\mathrm{.}00$ cm has its speed reduced by $10\%$ due to air resistance when the initial speed is of $45\mathrm{.}0$ m$/$s as it travels from the launch site to the target a distance of $18\mathrm{.}0$ m away. Due to the air resistance, a change in temperature occurs initially only for the air in a cylinder equal to the volume of air swept out by the sphere. Determine the maximum possible temperature change $($in $$C$)$ for this air when the temperature of the air is $20\mathrm{.}0$C$.$ To find the greatest possible temperature change, you may make the following assumptions: air has a molar specific heat of

CV $=$

$52$

R$,$

an equivalent molar mass of $28\mathrm{.}9$ g$/$mol$,$ and a density of $1\mathrm{.}20$ kg$/$m$3.$

$$C