# Question f4097

Aug 2, 2017

$\text{pressure} = 45.9$ $\text{psi}$

#### Explanation:

We're asked to find the final pressure of the gas, given its initial pressure, initial temperature, and final temperature.

We can use Gay-Lussac's law for this problem, which is

$\underline{\frac{{P}_{1}}{{T}_{1}} = \frac{{P}_{2}}{{T}_{2}}} \textcolor{w h i t e}{a a}$ (constant volume and quantity)

where

• ${P}_{1}$ is the initial pressure

• ${P}_{2}$ is the final pressure (what we're trying to find)

• ${T}_{1}$ is the initial absolute temperature (in Kelvin)

• ${T}_{2}$ is the final absolute temperature (in Kelvin)

We have:

• ${P}_{1} = 32.6$ $\text{psi}$

• P_2 = ?#

• ${T}_{1} = 735$ $\text{K}$

• ${T}_{2} = 1035$ $\text{K}$

Let's rearrange the above equation to solve for the final pressure, ${P}_{2}$:

${P}_{2} = \frac{{P}_{1} {T}_{2}}{{T}_{1}}$

Plugging in known values:

${P}_{2} = \left(\left(32.6 \textcolor{w h i t e}{l} \text{psi")(1035cancel("K")))/(735cancel("K")) = color(red)(ulbar(|stackrel(" ")(" "45.9color(white)(l)"psi"" }\right) |\right)$