Given:
[tex]P_{1} = \text{684 torr}[/tex]
[tex]T_{1} = \text{30°C + 273 = 303 K}[/tex]
[tex]P_{2} = \text{460 torr}[/tex]
Unknown:
[tex]T_{2}[/tex]
Solution:
[tex]\frac{P_{1}}{T_{1}} = \frac{P_{2}}{T_{2}}[/tex]
[tex]T_{2} = T_{1} × \frac{P_{2}}{P_{1}}[/tex]
[tex]T_{2} = \text{303 K} × \frac{\text{460 torr}}{\text{684 torr}}[/tex]
[tex]T_{2} = \text{204 K}[/tex]
[tex]T_{2} = \text{204 K} - 273[/tex]
[tex]\boxed{T_{2} = -\text{69°C}}[/tex]
[tex]\\[/tex]
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