Hydrogen becomes a liquid at \(20.27 \mathrm{~K}\). What is this temperature in (a) \({ }^{\circ} \mathrm{C}\) ? (b) \({ }^{\circ} \mathrm{F}\) ?

When converting temperatures from the Kelvin scale to the Celsius scale, the formula is quite straightforward: \[ \text{°C} = \text{K} - 273.15 \]
Kelvin is an absolute temperature scale, meaning it starts from absolute zero, the lowest temperature theoretically possible.
To convert a Kelvin temperature to Celsius, subtract 273.15 from the Kelvin value.
For Hydrogen, which becomes a liquid at 20.27 K, the conversion would be:
\[ \text{°C} = 20.27 \text{~K} - 273.15 = -252.88 \text{~°C} \]
So, 20.27 K is equivalent to -252.88 °C.

To convert temperatures from the Celsius scale to the Fahrenheit scale, use the formula: \[ \text{°F} = (\text{°C} \times \frac{9}{5}) + 32 \]
This formula first multiplies the Celsius temperature by 9/5 to adjust the scale, then adds 32 to shift the temperature to the Fahrenheit scale.
Using the Celsius temperature of -252.88 °C, we convert it as follows:
\[ \text{°F} = (-252.88 \times \frac{9}{5}) + 32 = -423.18 \text{~°F} \]
So, -252.88 °C is equivalent to -423.18 °F. This shows the much lower perception of the same temperature in different scales.

Understanding different temperature scales helps in various scientific and daily applications.
Let's briefly go over the three commonly used scales: Kelvin, Celsius, and Fahrenheit.

**Kelvin Scale**
- The Kelvin scale is an absolute temperature scale starting from absolute zero (0 K).
- It is mainly used in scientific contexts.

**Celsius Scale**
- The Celsius scale, based on water's freezing (0 °C) and boiling points (100 °C) under standard atmospheric pressure, is widely used in most of the world.
- It is part of the metric system.

**Fahrenheit Scale**
- The Fahrenheit scale, used primarily in the United States, defines 32 °F as the freezing point and 212 °F as the boiling point of water.
- Each degree Fahrenheit is an increment of 1/180th of the difference between the freezing and boiling points of water under standard conditions.

Understanding these scales and how to convert between them assists students in grasping how temperature is measured and compared globally.