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Maybelline Cousteau's backup oxygen tank reads 900 mmHg while on her boat, where the temperature is 27 degrees Celsius. When she dives down to the bottom of an unexpected methane lake on a recently discovered moon of Neptune, the temperature will drop down to 183 degrees Celsius. What will the pressure in her backup tank be at that temperature?

Sagot :

Given:

[tex]P_{1} = \text{900 mmHg}[/tex]

[tex]T_{1} = \text{27°C + 273 = 300 K}[/tex]

[tex]T_{2} = -\text{183°C + 273 = 90 K}[/tex]

Unknown:

[tex]P_{2}[/tex]

Solution:

[tex]\frac{P_{1}}{T_{1}} = \frac{P_{2}}{T_{2}}[/tex]

[tex]P_{2} = P_{1} × \frac{T_{2}}{T_{1}}[/tex]

[tex]P_{2} = \text{900 mmHg} × \frac{\text{90 K}}{\text{300 K}}[/tex]

[tex]\boxed{P_{2} = \text{270 mmHg}}[/tex]

[tex]\\[/tex]

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