Question

The space shuttle uses liquefied hydrogen at a temperature of \(-422^{\circ} \mathrm{F}\). What is the Kelvin temperature?

Short answer

The Kelvin temperature is approximately 20.93 K.

Step-by-step solution

Understand the Conversion Formula

To convert a temperature from Fahrenheit to Kelvin, we first need to convert it to Celsius using the formula: \[ C = \frac{5}{9} (F - 32) \]where \(F\) is the temperature in Fahrenheit. Then, convert Celsius to Kelvin using:\[ K = C + 273.15 \]This step establishes the relationship between the different temperature scales.

Convert Fahrenheit to Celsius

Substitute \(-422^{\circ}F\) into the Celsius conversion formula:\[ C = \frac{5}{9} (-422 - 32) \]Calculate the expression inside the parentheses first:\(-422 - 32 = -454\).Now, compute the Celsius value:\[ C = \frac{5}{9} \times (-454) = -252.22 \] approximately.This gives us the temperature in Celsius.

Convert Celsius to Kelvin

Now, convert the temperature from Celsius to Kelvin using the formula:\[ K = C + 273.15 \]Substitute \(-252.22\) for \(C\):\[ K = -252.22 + 273.15 = 20.93 \]This gives us the temperature in Kelvin, rounded to two decimal places.

Key concepts

Fahrenheit to Kelvin

When dealing with temperature conversions, it's important to understand the different scales and how they relate to each other. The Fahrenheit and Kelvin scales are two such systems. Fahrenheit is commonly used in the United States while Kelvin is essential for scientific calculations. To convert Fahrenheit to Kelvin, you must first convert the temperature to Celsius.

This is because there is no direct formula to convert Fahrenheit to Kelvin. Instead, use the two-step method. First, apply the formula:

• Convert Fahrenheit to Celsius using: \[C = \frac{5}{9} (F - 32)\]
• Then, convert Celsius to Kelvin using: \[K = C + 273.15\]

Once you finish this process, you'll have successfully converted a Fahrenheit temperature into Kelvin.

Celsius conversion formula

The Celsius conversion formula is an essential mathematical formula that helps in temperature conversions from Fahrenheit to Celsius. This formula is derived from the principle that each increment on the Celsius scale corresponds to an increment of nine-fifths on the Fahrenheit scale. According to this logic:
\[C = \frac{5}{9} (F - 32)\]This formula essentially reflects the operation of subtracting 32 from the Fahrenheit value,
then scaling down by multiplying by the fraction \(\frac{5}{9}\),
to account for the difference in scale size between Fahrenheit and Celsius.

This approach ensures that you align the temperature scales correctly, allowing for the precise conversion needed in scientific practices. Remember, understanding how each step affects the calculation helps ensure accuracy when you do the conversion.

Kelvin temperature calculation

The Kelvin scale is widely used in scientific and academic contexts due to its absolute nature. To calculate a Kelvin temperature, one begins with a Celsius temperature. The conversion is straightforward,
with the formula:
\[K = C + 273.15\]This formula reflects the fact that zero Kelvin, or absolute zero, corresponds to \(-273.15^{\circ}C\). By adding 273.15 to the Celsius value, any temperature can be seamlessly transitioned into the Kelvin scale.

This step is quite simple but crucial, particularly in physics and chemistry,
where calculations often require the use of absolute temperatures. As such, having a precise Kelvin value is important for accuracy in these fields,
as even minor errors in temperature conversion could lead to significant discrepancies in experiments and outcomes.