According to Gay Lussac's law, the pressure of a given mass of gas is directly proportional to its temperature provided that volume is constant. Mathematically;
[tex]\begin{gathered} P\alpha T \\ P=kT \\ k=\frac{P}{T} \\ k=\frac{P_1}{T_1}=\frac{P_2}{T_2} \end{gathered}[/tex]From the given question, we are given the following parameters:
[tex]\begin{gathered} P_1=20psi \\ T_1=24^0C=24+273=297K \\ T_2=480^0C=480+273=753K \\ P_2=\text{?} \end{gathered}[/tex]Substitute the given parameters into the formula as shown:
[tex]\begin{gathered} P_2=\frac{P_1T_2}{T_1} \\ P_2=\frac{20psi\times753\cancel{K}}{297\cancel{K}} \\ P_2=\frac{15,060}{297} \\ P_2=50.71\text{psi} \end{gathered}[/tex]Therefore the pressure of the spray paint at 480 celsius is 50.71psi
