An arctic weather balloon is filled with 12.1L of helium gas inside a prep shed. The temperature inside the shed is 9.°C. The balloon is then taken outside, where the temperature is −7.°C. Calculate the new volume of the balloon. You may assume the pressure on the balloon stays constant at exactly 1atm. Round your answer to 3 significant digits.

Charles' Law : It is defined as the volume of gas is directly proportional to the temperature of the gas at constant pressure and number of moles.

[tex]V\propto T[/tex]

or,

[tex]\frac{V_1}{V_2}=\frac{T_1}{T_2}[/tex]

where,

[tex]V_1[/tex] = initial volume of gas = 12.1 L

[tex]V_2[/tex] = final volume of gas = ?

[tex]T_1[/tex] = initial temperature of gas = [tex]9^oC=273+9=282K[/tex]

[tex]T_2[/tex] = final temperature of gas = [tex]-7^oC=273+(-7)=266K[/tex]

Now put all the given values in the above formula, we get the final volume of the gas.

[tex]\frac{12.1L}{V_2}=\frac{282K}{266K}[/tex]

[tex]V_2=11.4L[/tex]

Therefore, the new or final volume of gas will be, 11.4 L