Problem 43 - General Chemistry: Principles and Modern Applications

Question

The absolute zero of temperature is \(-273.15^{\circ} \mathrm{C}\) Should it be possible to achieve a temperature of \(-465^{\circ} \mathrm{F} ?\) Explain.

Step-by-Step Solution

Answer

Yes, a temperature of -465°F, equivalent to -268.33°C, is above the absolute zero of temperature (-273.15°C) and therefore is theoretically possible.

Step 1: Understand the Temperature Comparison

You know that the absolute zero of temperature is -273.15°C. This exercise is asking if it's possible to reach a temperature of -465°F

Step 2: Convert Fahrenheit to Celsius

In order to compare -465°F to -273.15°C, they should use the same measurement. Convert -465°F to Celsius using the formula \(C = (F - 32) * (5/9)\). Computing, you get \[ C = (-465 - 32) * (5/9) = -268.33 \text{°C} \]

Step 3: Compare the Calculated Value with Absolute Zero

Now that -465°F is converted to -268.33°C, you can see that -268.33°C is greater than the absolute zero of -273.15°C. This means that a temperature of -465°F is theoretically above absolute zero, and is theoretically possible.

Key Concepts

Temperature Conversion Essentials

Converting temperatures between different units, like Celsius and Fahrenheit, is a common necessity in science and everyday life. Understanding the conversion process helps in comparing temperatures from different scales effectively. The main formula used for this conversion is:

• Celsius to Fahrenheit: \( F = C \times \frac{9}{5} + 32 \)
• Fahrenheit to Celsius: \( C = (F - 32) \times \left(\frac{5}{9}\right) \)

These formulas work by adjusting for the starting point and range differences between the two units. The Fahrenheit scale starts at 32 for the freezing point of water and rises to 212 at its boiling point, creating an uneven relationship compared to the Celsius scale.

Converting Fahrenheit to Celsius

In this exercise, converting -465°F to Celsius allows for direct comparison to the absolute zero of -273.15°C. Using the formula for Fahrenheit to Celsius conversion, we have:\[C = (F - 32) \times \left(\frac{5}{9}\right)\]Substituting -465 for F, we calculate:\[C = (-465 - 32) \times \left(\frac{5}{9}\right) = -497 \times \left(\frac{5}{9}\right) = -268.33 \, °C\]This value tells us more accurately where -465°F stands on the Celsius scale, bringing it close to absolute zero, but not quite reaching it.

Exploring Theoretical Temperature Limits

Absolute zero is a fundamental concept in science. It represents the lowest possible temperature, -273.15°C, where the particles of a substance theoretically have minimal vibration and virtually no thermal energy. This concept marks the boundary of temperature as traditionally understood. Theoretically, no temperature can be lower than absolute zero. This constraint arises from the principles of thermodynamics, specifically the third law, stating that it's impossible to reach absolute zero through any finite number of physical processes. The exercise confirms -465°F corresponds to -268.33°C, above absolute zero. So, while practically very low, this temperature is theoretically achievable compared to absolute zero's limit.