Question

Make the following temperature conversions: a. 44.2 ' C to kelvins b. \(891 \mathrm{~K}\) to \(\mathrm{C}\) c. -20 " to kelvins d. \(273.1 \mathrm{~K}\) to \(\mathrm{C}\)

Short answer

a. \(44.2^\circ C = 317.35 K\) b. \(891 K = 617.85^\circ C\) c. \(-20^\circ F = 244.82 K\) d. \(273.1 K = -0.05^\circ C\)

Step-by-step solution

Part a: 44.2°C to Kelvin

To convert 44.2°C to Kelvin, use the Celsius to Kelvin formula: Kelvin (K) = Celsius (C) + 273.15 K = 44.2 + 273.15 K = 317.35 So, 44.2°C is equal to 317.35 K.

Part b: 891 K to Celsius

To convert 891 K to Celsius, use the Kelvin to Celsius formula: Celsius (C) = Kelvin (K) - 273.15 C = 891 - 273.15 C = 617.85 So, 891 K is equal to 617.85°C.

Part c: -20°F to Kelvin

To convert -20°F to Kelvin, use the Fahrenheit to Kelvin formula: Kelvin (K) = (Fahrenheit (F) + 459.67) * (5/9) K = (-20 + 459.67) * (5/9) K = (439.67) * (5/9) K = 244.82 So, -20°F is equal to 244.82 K.

Part d: 273.1 K to Celsius

To convert 273.1 K to Celsius, use the Kelvin to Celsius formula: Celsius (C) = Kelvin (K) - 273.15 C = 273.1 - 273.15 C = -0.05 So, 273.1 K is equal to -0.05°C.

Key concepts

Celsius to Kelvin Conversion

Understanding how to convert temperatures from Celsius to Kelvin can be quite handy, especially in scientific contexts where Kelvin is often used. The key formula to remember is:

\[ \text{Kelvin (K) = Celsius (C) + 273.15} \]
This formula stems from the zero points of the two scales: 0°C corresponds to 273.15K, which is the absolute zero in the Celsius scale. Let's take an exercise example, converting 44.2°C to Kelvin:

You add the constant number, 273.15, to the Celsius value to get the Kelvin temperature. So, \( 44.2 \text{°C} + 273.15 \) gives us \( 317.35 \text{K} \).

Remember not to include the 'degree' symbol when writing Kelvin temperatures, as it is an absolute scale, not relative like Celsius or Fahrenheit. This simple addition helps students quickly adapt to this scale which is crucial for understanding scientific phenomena, such as thermodynamics and particle physics.

Kelvin to Celsius Conversion

When you're working in the opposite direction, converting temperatures from Kelvin to Celsius, the process is straightforward yet equally important. The formula to make this conversion is:

\[ \text{Celsius (C) = Kelvin (K) - 273.15} \]
This conversion is useful in a variety of scientific calculations and real-life applications like climate studies. To illustrate, let's examine how to convert 891 K to Celsius. According to our formula: \( 891 \text{K} - 273.15 \) equals \( 617.85 \text{°C} \).

Always subtract 273.15 from the Kelvin temperature to find the corresponding temperature in Celsius. It's a simple subtraction that reveals the relationship between the two units. The exact value of 273.15 is significant as it represents the precise difference between the two scales' zero points.

Fahrenheit to Kelvin Conversion

The conversion from Fahrenheit to Kelvin might seem tricky at first glance, but once you understand the formula, it's a smooth process. This transition is less common in day-to-day life but it is essential in scientific environments where precise and consistent units are required. The conversion formula is:

\[ \text{Kelvin (K) = (Fahrenheit (F) + 459.67) \times \frac{5}{9}} \]
This calculation includes two steps: firstly, adjusting the Fahrenheit temperature by adding 459.67 to it, and secondly, multiplying the result by \( \frac{5}{9} \) to convert it to the Kelvin scale. For instance, to convert -20°F to Kelvin, the formula yields \( (-20 + 459.67) \times \frac{5}{9} \) which results in \( 244.82 \text{K} \).

Remembering this formula is crucial for understanding global temperature scales and making accurate measurements in research and weather reporting. This conversion helps bridge the gap between the Fahrenheit scale, commonly used in the United States, and the Kelvin scale, which is an international standard for scientific measurements.