A container with a volume of 42 L contains a gas with a temperature of 150^o K. If the temperature of the gas changes to 75 ^o K without any change in pressure, what must the container's new volume be?
1 Answer
Explanation:
We're asked to find the final volume of a gas, given information about the temperature and volume.
To do this, we can use the temperature-volume relationship of gases, illustrated by Charles's law:
ulbar(|stackrel(" ")(" "(T_1)/(V_1) = (T_2)/(V_2)" ")|)
where
-
T_1 andT_2 are the initial and final absolute temperatures of the gas system (which must be in units of Kelvin) -
V_1 andV_2 are the initial and final volumes of the gas
We know:
-
V_1 = 42 "L" -
T_1 = 150 "K" -
V_2 = ? -
T_2 = 75 "K"
Let's rearrange the equation to solve for the final volume*,
V_2 = (T_2V_1)/(T_1)
Plugging in known values:
V_2 = ((75cancel("K"))(42color(white)(l)"L"))/(150cancel("K")) = color(red)(ulbar(|stackrel(" ")(" "21color(white)(l)"L"" ")|)
The final volume of the gas container is thus