Question

A spray paint can at 24 Celsius has a pressure of 20 psi. If it is placed in a fire at 480 Celsius what will the pressure become?

Answer 1

`50.71\text{psi}`

Explanations:

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;

`\begin{gathered} P\alpha T \\ P=kT \\ k=(P)/(T) \\ k=(P_1)/(T_1)=(P_2)/(T_2) \end{gathered}`

From the given question, we are given the following parameters:

`\begin{gathered} P_1=20psi \\ T_1=24^0C=24+273=297K \\ T_2=480^0C=480+273=753K \\ P_2=\text{?} \end{gathered}`

Substitute the given parameters into the formula as shown:

`\begin{gathered} P_2=(P_1T_2)/(T_1) \\ P_2=\frac{20psi*753\cancel{K}}{297\cancel{K}} \\ P_2=(15,060)/(297) \\ P_2=50.71\text{psi} \end{gathered}`

Therefore the pressure of the spray paint at 480 celsius is 50.71psi