Data:
[tex]V_{initial} = 4.9\:L[/tex]
[tex]T_{initial} = 30^0C[/tex]
converting to Kelvin
TK = TC + 273
TK = 30 + 273 → TK = 303 → [tex]T_{initial} = 303\:K[/tex]
[tex]V_{final} = ? (in\:liters)[/tex]
[tex]T_{final} = 199^0C[/tex]
TK = TC + 273
TK = 199 + 273 → TK = 472 → [tex]T_{final} = 472\: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{ 4.9 }{ 303 } = \frac{ V_{f} }{ 472 }[/tex]
Product of extremes equals product of means:
[tex]303* V_{f} = 4.9*472[/tex]
[tex]303 V_{f} = 2312.8[/tex]
[tex]V_{f} = \frac{2312.8}{303} [/tex]
[tex]\boxed{\boxed{V_{f} \approx 7.63\:L}}\end{array}}\qquad\quad\checkmark[/tex]
