Question

Question #f4097

Answer 1

`"pressure" = 45.9` `"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

`ul((P_1)/(T_1) = (P_2)/(T_2))color(white)(aa)` (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` `"psi"`

• `P_2 = ?`

• `T_1 = 735` `"K"`

• `T_2 = 1035` `"K"`

Let's rearrange the above equation to solve for the final pressure, `P_2`:

`P_2 = (P_1T_2)/(T_1)`

Plugging in known values:

`P_2 = ((32.6color(white)(l)"psi")(1035cancel("K")))/(735cancel("K")) = color(red)(ulbar(|stackrel(" ")(" "45.9color(white)(l)"psi"" ")|)`