An automobile tire has a volume of 1.63 x 10-2 m3 and contains air at a gauge pressure (pressure above atmospheric pressure) of 165 kpa when the temperature is 0.00°c. what is the gauge pressure of the air in the tires when its temperature rises to 27.3°c and its volume increases to 1.70 x 10-2 m3

 The gauge pressure of the air in the tires is 179.5 kPa.

Solution :

Combined gas law is the combination of Boyle's law, Charles's law and Gay-Lussac's law.

The combined gas equation is,

where,

= initial pressure of gas = Atmospheric pressure + gauge pressure = 101 kPa + 165 kPa = 266 kPa  

= final pressure of gas = ?

= initial volume of gas =

= final volume of gas =

= initial temperature of gas =

= final temperature of gas =

Now put all the given values in the above equation, we get the final pressure of gas.

Gauge pressure = Absolute pressure - atmospheric pressure  = (280.5 - 101) kPa= 179.5 kPa

Therefore, the gauge pressure of the air in the tires is 179.5 kPa.

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