Question

It's cold--check your tires.

When it gets cold, you have to add more air to car tires. If a 1.90×10⁻² m3m3  car tire at 299 KK  has an *absolute* pressure of only 213 kPa

How many moles of air do you have to add to increase its *absolute* pressure to 271 kPa? The temperature and volume of the tire remain constant.

Answer 1

We know the ideal gas equation

                                   PV = nRT

Where P is pressure, V is volume, n is number of moles of the gas, T is temperature, R=8.314 J/mol.K

is universal gas constant.

Initial condition of the system was

                                    V = 0.0190 m3 , P = 213 kPa, T = 299 K

So,

                                  

The final state of the system is

                                  T = 299 K, V = 0.0190 m3 , Pf = 271 kPa

SO,

                                 

So, to increase the pressure we need to add 2.07-1.63 = 0.44 mol of air.