Problem 93 - Chemistry: Atoms First

Question

Convert the boiling temperature of gold, \(2966^{\circ} \mathrm{C}\), into degrees Fahrenheit and kelvin.

Step-by-Step Solution

Answer

The boiling temperature of gold is \(5356.8^{\text{o}}F\) in Fahrenheit and \(3239.15 K\) in Kelvin.

Step 1: Convert Celsius to Fahrenheit

To convert degrees Celsius to degrees Fahrenheit, use the formula: \(F = \frac{9}{5}C + 32\). Plug the boiling temperature of gold in Celsius, \(2966^{\text{o}}C\), into the formula: \( F = \frac{9}{5} \times 2966 + 32\).

Step 2: Calculate Fahrenheit Temperature

Perform the multiplication and addition: \( F = \frac{9}{5} \times 2966 + 32 = 5324.8 + 32 = 5356.8\). Therefore, the boiling temperature of gold in Fahrenheit is \(5356.8^{\text{o}}F\).

Step 3: Convert Celsius to Kelvin

To convert degrees Celsius to Kelvin, use the formula: \( K = C + 273.15\). For the boiling temperature of gold, plug \(2966^{\text{o}}C\) into the formula: \( K = 2966 + 273.15\).

Step 4: Calculate Kelvin Temperature

Perform the addition: \( K = 2966 + 273.15 = 3239.15\). Therefore, the boiling temperature of gold in Kelvin is \(3239.15 K\).

Key Concepts

Celsius to Fahrenheit Conversion

Understanding the conversion from Celsius to Fahrenheit is essential for students and professionals dealing with temperature measurements. The relationship between these two temperature scales can be navigated using the formula: \( F = \frac{9}{5}C + 32 \). This equation reflects that Fahrenheit and Celsius scales intersect at -40 degrees, where they are equal.
When converting the boiling temperature of gold, which is exceptionally high at \(2966^{\text{o}}C\), the process involves multiplying the Celsius temperature by 9/5, then adding 32 to the result. For example:

1. Start with the boiling point of gold in Celsius: \(2966^{\text{o}}C\)
2. Multiply by 9/5: \( \frac{9}{5} \times 2966 = 5324.8 \)
3. Add 32 to calibrate to the Fahrenheit scale: \(5324.8 + 32 = 5356.8^{\text{o}}F\)

This precise conversion ensures accurate temperature reporting, especially important in high-temperature applications such as metallurgy and material science.

Celsius to Kelvin Conversion

The Celsius to Kelvin conversion is fundamental in scientific studies where absolute temperature measurement is required. Kelvin is the base unit of temperature in the International System of Units (SI), and it does not have degrees or negative numbers, representing a scale starting from absolute zero.
The simple formula to convert Celsius to Kelvin is \( K = C + 273.15 \). This formula implies that 0 degrees Celsius is equivalent to 273.15 Kelvin. The .15 represents the slight difference in the size of one degree on each scale and aligns with the absolute zero of the Kelvin scale.
For example, when converting the boiling temperature of gold, the calculation follows as:

1. Take the boiling temperature in Celsius: \(2966^{\text{o}}C\)
2. Add 273.15 to reach the Kelvin scale: \(2966 + 273.15 = 3239.15 K \)

With this understanding, students can confidently translate temperature information to the Kelvin scale, which is vital for thermodynamic equations and many scientific calculations.

Boiling Temperature of Gold

The boiling temperature of gold is a high-value data point in the field of chemistry and material sciences, signifying the temperature at which gold transitions from a liquid to a gaseous state. This temperature is an impressive \(2966^{\text{o}} C\), reflecting the extreme durability and stability of gold under intense heat.
Gold's boiling point is much higher compared to everyday substances, highlighting its unique applications in industries that require materials to withstand great thermal stress. Understanding the boiling temperature aids in applications from jewelry crafting to space technology where gold can act as a protective coating for satellites.
The knowledge of converting this boiling point to other scales—Fahrenheit for everyday use in the US and Kelvin for scientific purposes—empowers individuals to apply this concept globally. Such high-temperature conversions reinforce the importance of precision in calculations, ensuring that processes involving gold are carried out safely and effectively.