Data:
[tex]V_{initial} = 32.0\:cm^3[/tex]
[tex]T_{initial} = 189\:K[/tex]
[tex]V_{final} = ? [/tex]
[tex]T_{final} = 242\:K[/tex]
By the first Law of Charles and Gay-Lussac, we have:
[tex] \frac{ V_{i} }{ T_{i} } = \frac{ V_{f} }{ T_{f} }[/tex]
Solving:
[tex] \frac{ V_{i} }{ T_{i} } = \frac{ V_{f} }{ T_{f} }[/tex]
[tex]\frac{ 32.0 }{ 189\:K } = \frac{ V_{f} }{ 242 }[/tex]
Product of extremes equals product of means:
[tex]189* V_{f} = 32.0*242[/tex]
[tex]189 V_{f} = 7744[/tex]
[tex]V_{f} = \frac{7744}{189} [/tex]
[tex]V_{f} = 40.97354...\to \boxed{V_{f} \approx 41\:cm^3}[/tex]
