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Chapter 1: Problem 105

The hottest temperature recorded in the United States is \(134^{\circ} \mathrm{F}\) in Greenland Ranch, CA. The melting point of phosphorus is \(44^{\circ} \mathrm{C}\). At this temperature, would phosphorus be a liquid or a solid?

Short Answer

Expert verified
At the hottest temperature recorded in the United States, which is approximately \(56.67^{\circ}\mathrm{C}\), phosphorus would be in a liquid state, as it exceeds its melting point of \(44^{\circ}\mathrm{C}\).

Step by step solution

01

Convert the temperature from Fahrenheit to Celsius

To convert the temperature from Fahrenheit to Celsius, we use the formula: \[ \mathrm{C} = \frac{5}{9}(\mathrm{F} - 32) \] Where (C) is the temperature in Celsius, and (F) is the temperature in Fahrenheit. In this case, F = \(134^{\circ}\mathrm{F}\). So, \[ \mathrm{C} = \frac{5}{9}(134 - 32) \]
02

Calculate the Celsius temperature

We need to perform the operations inside the parentheses first and then multiply the result by \(\frac{5}{9}\): \[ \mathrm{C} = \frac{5}{9}(102) \] Now, multiply by \(\frac{5}{9}\): \[ \mathrm{C} \approx 56.67 ^{\circ}\mathrm{C} \] So, the hottest temperature recorded in the United States is approximately \(56.67^{\circ}\mathrm{C}\).
03

Compare the temperature with the melting point of phosphorus

The melting point of phosphorus is \(44^{\circ}\mathrm{C}\). Since the hottest temperature recorded in the United States (\(56.67^{\circ}\mathrm{C}\)) is higher than the melting point of phosphorus (\(44^{\circ}\mathrm{C}\)), phosphorus would be a liquid at this temperature.

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