Question $2.[6$ marks$]$

A car's tire depends on the temperature of the air in the tire. When this air temperature is $25C,$ the pressure gage reads $210$ kPa $.$ If the volume of the tire is $0\mathrm{.}025m3,$ determine the pressure rise in the tire when the air temperature in the tire rises to $50C.$ Also, determine the amount of air that must be bled off $($released to the atmosphere$)$ to restore pressure to its original value at this temperature. Assume the atmospheric pressure to be $100$ kPa $.$

Properties The gas constant of air is $R=0\mathrm{.}287\frac{(kJ)}{(kg)*(K)}(\frac{\text{k}\text{P}\text{a}*m^3}{(kJ)})=0\mathrm{.}287\frac{\text{k}\text{P}\text{a}*m^3}{(kg)*(K)}.$