Question

Question #56270

Answer 1

`"temperature" = 2497` `""^"o""C"`

Explanation:

We're asked to find the final temperature of the gas, given its initial pressure, final pressure, and initial 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 = 575` `"torr"`

• `P_2 = 5750` `"torr"`

• `T_1 = 4` `""^"o""C"` `+ 273 = ul(277color(white)(l)"K"`

• `T_2 = ?`

Let's rearrange the above equation to solve for the final temperature, `T_2`:

`T_2 = (T_1P_2)/(P_1)`

Plugging in known values:

`T_2 = ((277color(white)(l)"K")(5750cancel("torr")))/(575cancel("torr")) = color(red)(ul(2770color(white)(l)"K"`

Which, in `""^"o""C"`, is

`T_2 = color(red)(2770color(white)(l)"K") - 273 = color(blue)(ulbar(|stackrel(" ")(" "2497color(white)(l)""^"o""C"" ")|)`