A balloon takes up 624L at 0 degrees Celsius. If it is heated to 80 degrees Celsius, what will its volume be?

The variables are volume and temperature, so this is an example of Charles' law which states that the volume of a given amount of gas held at constant pressure is directly proportional to the Kelvin temperature. This means that if the volume increases, so does the temperature, and vice versa. The equation for Charles' law is:

#V_1/T_1=V_2/T_2#

Known

#V_1="624 L"#

#T_1="0"^@"C + 273.15"="273 K"#

#T_2="80"^@"C + 273.15"="353 K"#

Unknown

#V_2#

Solution

Rearrange the equation to isolate #V_2#. Plug in the known value and solve.

#V_2=(V_1T_2)/T_1#

#V_2=(624"L"xx353color(red)cancel(color(black)("K")))/(273color(red)cancel(color(black)("K")))="807 L"# rounded to three significant figures

We know that as constant pressure, and constant quantity of gas, #VpropT#..i.e. #V=kT#...where #k# is some constant of proportionality.. But this should hold for ALL conditions of temperature. And so we solve for #k#...and so #V_1/T_1=V_2/T_2#; temperature is specified on the absolute scale....#0*K-=-273.15# #""^@C#...

And so #V_2=V_1/T_1xxT_2=(624*L)/(273.15*K)xx353.15*K#..

We gets #V_2~=800*L#...