Answer :
If the tire volume is constant, the pressure (in psi) is 37.72psi.
We are given the following information:
- The initial temperature of the air, [tex]$T_{1}=295 \mathrm{~K}$[/tex]
- The initial pressure, [tex]$P_{1}=35.0 \mathrm{psi}$[/tex]
- The initial volume, [tex]$V_{1}=218 \mathrm{~L}$[/tex]
- The final temperature, [tex]$T_{2}=318 \mathrm{~K}$[/tex]
- The increase in the volume is constant.
The combined gas law states that a fixed amount of an ideal gas obeys the following equation: [tex]$\frac{P V}{T}=$[/tex]constant, where:
- P is the Pressure of the gas.
- V is the Volume of the gas.
- n is the number of moles of gas.
-[tex]$R=8.31 \mathrm{~J} / \mathrm{mol} \mathrm{K}=0.0821 \mathrm{~L} \cdot \mathrm{atm} / \mathrm{mol} \cdot \mathrm{K}$[/tex] is the Universal Gas constant.
- T is the absolute temperature of the gas.
Equating the initial and final state, we have:
[tex]$\begin{aligned}\frac{P_{2} V_{2}}{T_{2}} &=\frac{P_{1} V_{1}}{T_{1}} \\\Rightarrow P_{2} &=\frac{V_{1}}{V_{2}} \times \frac{T_{2}}{T_{1}} \times P_{1} \\&=\frac{V_{1}}{ V_{1} } \times \frac{318 \mathrm{~K}}{295 \mathrm{~K}} \times 35.0 \mathrm{psi}\end{aligned}$[/tex]
=37.72psi
The ideal gas law states that a universal constant for an ideal gas is the ratio of the product of pressure and temperature to the product of the number of moles and absolute temperature. The resultant equation is known as the combined gas law if the number of moles in the ideal gas law is set to a constant.
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