Problem 3 - Chemistry

Question

The melting point of table salt is \(1474^{\circ} \mathrm{F}\). What temperature is this on the Celsius and Kelvin scales?

Step-by-Step Solution

Answer

The melting point is approximately \(801.11^{\circ} \mathrm{C}\) and \(1074.26 \mathrm{K}\).

Step 1: Convert Fahrenheit to Celsius

To convert from Fahrenheit to Celsius, we use the formula \( C = \frac{5}{9}(F - 32) \). Plugging the given melting point of table salt \( F = 1474^{\circ} \mathrm{F} \) into the formula, we calculate:\[C = \frac{5}{9} (1474 - 32) = \frac{5}{9} \times 1442 = 801.11^{\circ} \mathrm{C}\] Thus, the melting point in Celsius is approximately \(801.11^{\circ} \mathrm{C}\).

Step 2: Convert Celsius to Kelvin

To convert from Celsius to Kelvin, we use the formula \( K = C + 273.15 \). Using the Celsius value from the previous step \( C = 801.11^{\circ} \mathrm{C} \), we calculate:\[K = 801.11 + 273.15 = 1074.26 \mathrm{K}\] Hence, the melting point is \(1074.26 \mathrm{K}\).

Key Concepts

Fahrenheit to Celsius conversion

Temperature conversion is a common task in science and everyday life. One of the most frequently needed conversions is from Fahrenheit to Celsius. This simple process allows us to understand temperatures in a more global context. To convert a temperature from Fahrenheit (F) to Celsius (C), we use the formula:

• \[ C = \frac{5}{9}(F - 32) \]

This means that we first subtract 32 from the Fahrenheit temperature. This step corrects for the different starting points of the Fahrenheit scale. Next, multiplying by 5/9 adjusts for the different size of the Fahrenheit and Celsius degrees. For example, to find the melting point of table salt given as \(1474^{\circ} \text{F}\), simply substitute into the formula:

• \[ C = \frac{5}{9} \times (1474 - 32) = 801.11^{\circ} \text{C} \]

By following these steps, you can convert temperatures between these two scales with ease.

Celsius to Kelvin conversion

Understanding temperature on the Kelvin scale is essential for scientists and engineers. Kelvin is the SI unit for temperature used in scientific calculations. Unlike Celsius and Fahrenheit, Kelvin starts at absolute zero, the lowest possible temperature where all thermal motion ceases. To convert a temperature from Celsius (C) to Kelvin (K), use the following straightforward formula:

• \[ K = C + 273.15 \]

This conversion simply involves adding 273.15 to the Celsius temperature. This number bridges the gap between the Celsius scale and the Kelvin scale. For instance, using our previous conversion result of \(801.11^{\circ} \text{C}\) from the table salt melting point, the Kelvin temperature is:

• \[ K = 801.11 + 273.15 = 1074.26 \text{K} \]

With this easy conversion, temperatures can be accurately communicated and calculated.

Melting point calculation

Melting points are crucial in materials science, determining the temperatures at which substances transition from solid to liquid. Understanding how to calculate and convert melting points into different temperature scales helps in a variety of applications, from industrial processing to academic research. Begin by identifying the melting point in an accessible temperature scale. Then use the conversion formulas:

• Fahrenheit to Celsius: \( C = \frac{5}{9}(F - 32) \)
• Celsius to Kelvin: \( K = C + 273.15 \)

For example, if the melting point of a substance is given as \(1474^{\circ} \text{F}\), convert it into Celsius and then to Kelvin to obtain well-rounded understanding. After determining the Celsius equivalent \(801.11^{\circ} \text{C}\), you can easily convert to Kelvin \(1074.26 \text{K}\). This approach not only gives a numerical evaluation but also displays consistency across different scientific fields.