Question

The gas inside of a container exerts `12 Pa` of pressure and is at a temperature of `360 ^o K`. If the pressure in the container changes to `64 Pa` with no change in the container's volume, what is the new temperature of the gas?

Answer 1

`T_2 = 1920` `"K"`

Explanation:

We're asked to find the final temperature of a gas, given some pressure and temperature information.

To do this, we can use the pressure-temperature relationship of gases, illustrated by Gay-Lussac's law:

`(P_1)/(T_1) = (P_2)/(T_2)" "` (constant volume and quantity of gas)

where

• `P_1` and `P_2` are the initial and final pressures of the gas

• `T_1` and `T_2` are the initial and final absolute temperatures of the gas (which must be in Kelvin)

We know:

• `P_1 = 12` `"Pa"`

• `P_2 = 64` `"Pa"`

• `T_1 = 360` `"K"`

• `T_2 = ?`

Plugging these in:

`(12color(white)(l)"Pa")/(360color(white)(l)"K") = (64color(white)(l)"Pa")/(T_2)`

`color(red)(ulbar(|stackrel(" ")(" "T_2 = 1920color(white)(l)"K"" ")|)`