Problem 19 - Chemistry and Chemical Reactivity

Question

Make the following temperature conversions: $$\begin{array}{ll} \hline \mathrm{C} & \mathrm{K} \\ \hline \text { a) } 16 & \\ \text { (b) } & 370 \\ \text { (c) } 40 & \\ \text {} \end{array}$$

Step-by-Step Solution

Answer

16°C = 289.15K; 370K = 96.85°C; 40°C = 313.15K.

Step 1: Introduction to Temperature Conversion Formulas

To convert temperatures between Celsius and Kelvin, use the formula: \( K = C + 273.15 \) to convert Celsius to Kelvin, and \( C = K - 273.15 \) to convert Kelvin to Celsius.

Step 2: Convert 16°C to Kelvin

Using the formula \( K = C + 273.15 \), substitute 16 for \( C \): \( K = 16 + 273.15 \). Therefore, 16°C is \( 289.15 \)K.

Step 3: Convert 370 K to Celsius

Using the formula \( C = K - 273.15 \), substitute 370 for \( K \): \( C = 370 - 273.15 \). Therefore, 370K is \( 96.85 \)°C.

Step 4: Convert 40°C to Kelvin

Using the formula \( K = C + 273.15 \), substitute 40 for \( C \): \( K = 40 + 273.15 \). Therefore, 40°C is \( 313.15 \)K.

Key Concepts

Celsius to Kelvin

When you are converting temperature values from Celsius to Kelvin, you're adding a constant value to your Celsius measurement to account for the difference in the starting points of the two scales. The reason for this offset is because Kelvin, unlike Celsius, uses absolute zero as its zero point—this represents the point where all kinetic motion within atoms essentially stops.
This means that the Kelvin scale does not have negative numbers, which can often make it more convenient for scientific calculations.
To perform the conversion, you use the formula:

• \( K = C + 273.15 \)

In simpler terms:

• Add 273.15 to the Celsius value.

For example, if you start with 16°C:

• Add 273.15 to get \( 289.15 \)K.

This consistent offset is handy for converting temperatures quickly and accurately.

Kelvin to Celsius

Converting Kelvin to Celsius is practically the reverse process of converting Celsius to Kelvin. Since Kelvin temperatures already include that base offset of 273.15 from Celsius zero, you simply subtract this value to convert back to Celsius.Here's the simple formula:

• \( C = K - 273.15 \)

To put it plainly:

• Subtract 273.15 from the Kelvin value.

Consider you have a temperature of 370 Kelvin:

• Subtract 273.15 to find it equals \( 96.85 \)°C.

This method ensures your conversions are quick and precise, utilizing the relation between these interconnected scales.

Conversion Formulas

Understanding conversion formulas is the cornerstone of transforming temperatures between any two scales. For Celsius and Kelvin, these formulas are particularly straightforward and based on the fixed differences between the two scales' starting points.
Let’s delve into the formulas:

• Celsius to Kelvin: \( K = C + 273.15 \)
• Kelvin to Celsius: \( C = K - 273.15 \)

These formulas emerge from the definition of Kelvin as an absolute temperature scale, where 0 K represents absolute zero, or the cessation of all thermal motion. This makes Kelvin ideal for scientific work as it provides an accurate depiction of thermal dynamics.
By mastering these simple equations, you can easily transition between these temperature measurements, aiding your understanding of thermodynamics and various scientific processes.