Question

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

Answer 1

Answer:  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,

$\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}$

where,

$P_1$ = initial pressure of gas = Atmospheric pressure + gauge pressure = 101 kPa + 165 kPa = 266 kPa  

$P_2$ = final pressure of gas = ?

$V_1$ = initial volume of gas = $1.63\times 10^{-2}m^3$

$V_2$ = final volume of gas = $1.70\times 10^{-2}m^3$

$T_1$ = initial temperature of gas = $0^oC=273+0=273K$

$T_2$ = final temperature of gas = $27.3^oC=273+27.3=300.3K$

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

$\frac{266\times 1.63\times 10^{-2}}{273K}=\frac{P_2\times 1.70\times 10^{-2}}{300.3K}$

$P_2=280.5kPa$

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.