346.5cm³
According to Charles law, the volume of a given gas sample is directly proportional to its absolute temperature at constant pressure. Mathematically;
[tex]\begin{gathered} v\alpha T \\ v=kT \\ k=\frac{v_1}{T_1}=\frac{v_2}{T_2}_{}_{} \end{gathered}[/tex]where:
• v1 and v2 are the ,initial and final volume
,• T1 and T2 are the ,initial and final temperatures ,in Kelvin
Given the following parameters
• v1 = 417 cm³
,• T1 = 278K
,• T2 = 231K
Substitute the given parameters into the formula to get the final volume as shown:
[tex]\begin{gathered} v_2=\frac{v_1T_2}{T_1} \\ v_2=\frac{417\operatorname{cm}^3\times231\cancel{K}}{278\cancel{K}} \\ v_2=\frac{96,327}{278} \\ v_2=346.5\operatorname{cm}^3 \end{gathered}[/tex]Hence the new volume of the balloon will be 346.5cm³