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