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# and#T_2# are the initial and final absolute temperatures of the gas system (which must be in units of Kelvin) -
#V_1# and#V_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
