Problem 20 - Chemistry and Chemical Reactivity

Question

Make the following temperature conversions: $$\begin{array}{ll} \hline \mathrm{C} & \mathrm{K} \\ \hline \text { a) } & 77\\\ \text { (b) } 63 & \\ \text { (c) } & 1450 \\ \text {} \end{array}$$

Step-by-Step Solution

Answer

77°C = 350.15 K, 63°C = 336.15 K, 1450 K = 1176.85°C.

Step 1: Understand the formula

To convert a temperature from Celsius to Kelvin, use the formula: \[K = C + 273.15\]This formula adds 273.15 to the Celsius temperature to find the equivalent in Kelvin.

Step 2: Convert 77°C to Kelvin

Using the formula, add 273.15 to 77: \[K = 77 + 273.15 = 350.15\]Therefore, 77°C is equivalent to 350.15 K.

Step 3: Convert 63°C to Kelvin

Add 273.15 to 63:\[K = 63 + 273.15 = 336.15\]So, 63°C is equivalent to 336.15 K.

Step 4: Convert 1450 K to Celsius

To convert Kelvin to Celsius, use the formula:\[C = K - 273.15\]Subtract 273.15 from 1450:\[C = 1450 - 273.15 = 1176.85\]Thus, 1450 K is equivalent to 1176.85°C.

Key Concepts

Celsius to Kelvin

The Celsius to Kelvin conversion is a straightforward process that involves a simple addition. Celsius (\(^\circ C\)) and Kelvin (K) are both units of temperature, commonly used in scientific calculations, as well as in daily life. To transform a temperature from Celsius to Kelvin, you use the formula:\[ K = C + 273.15 \]This formula is quite intuitive. All you need to do is add 273.15 to the Celsius temperature. This adjustment accounts for the difference in the starting point of these temperature scales.

• Celsius begins at the freezing point of water, which is 0°C.
• Kelvin starts at absolute zero, the coldest theoretical temperature possible, which is -273.15°C.

Understanding that the formula involves only addition makes it easy to perform these conversions. So, whenever you have a temperature in Celsius, simply add 273.15 to convert it to Kelvin.

Kelvin to Celsius

Converting from Kelvin to Celsius is just as simple as the reverse process. Because Kelvin and Celsius scales are directly related, converting between them involves basic subtraction.To convert a temperature from Kelvin to Celsius, apply the following formula:\[ C = K - 273.15 \]This formula requires you to subtract 273.15 from the Kelvin temperature. This subtraction aligns the starting points of the two scales, ensuring the accuracy of the conversion.

• Kelvin measurements often begin from absolute zero, considered as 0 K.
• Celsius, on the other hand, starts at 0 for the freezing point of water.

By removing the 273.15 offset in the Kelvin scale, you can easily find the equivalent Celsius temperature. This method aids in transitioning temperatures from scientific contexts to everyday scenarios without confusion.

Conversion Formula

The conversion formulas for Celsius to Kelvin and Kelvin to Celsius are essential tools in temperature computations. As seen in scientific work, engineering applications, and meteorological studies, these conversions make temperature universally understandable across different domains.The straightforward formulas are: - For Celsius to Kelvin: \[ K = C + 273.15 \]- For Kelvin to Celsius: \[ C = K - 273.15 \]These formulas underscore the importance of the 273.15 value, which compensates for the different base points of the two scales.

This very consistency is what allows for accurate conversions across various contexts. By memorizing these simple equations, anyone can switch between the two temperature scales quickly and reliably. They simplify many practical problems, ensuring that whether you're recording experiments, adjusting climate control systems, or just curious about the weather, you have the right tools to do so effectively.