Question #56270

1 Answer
Aug 2, 2017

Answer:

#"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"" ")|)#