Question

Convert the following temperatures to degrees Celsius: (a) \(77 \mathrm{~K},\) the boiling point of liquid nitrogen, (b) \(4.22 \mathrm{~K}\) the boiling point of liquid helium, (c) \(600.61 \mathrm{~K},\) the melting point of lead.

Short answer

(a) -196.15°C, (b) -268.93°C, (c) 327.46°C.

Step-by-step solution

Understanding the Formula

To convert temperatures from Kelvin to Celsius, we use the formula: \[ C = K - 273.15 \]where \( C \) is the temperature in degrees Celsius and \( K \) is the temperature in Kelvin.

Convert 77 K to Celsius

Applying the formula, we substitute 77 for \( K \):\[ C = 77 - 273.15 = -196.15 \]Thus, the boiling point of liquid nitrogen is \(-196.15\, ^\circ C\).

Convert 4.22 K to Celsius

Using the formula, substitute 4.22 for \( K \):\[ C = 4.22 - 273.15 = -268.93 \]Therefore, the boiling point of liquid helium is \(-268.93\, ^\circ C\).

Convert 600.61 K to Celsius

Substitute 600.61 for \( K \) in the formula:\[ C = 600.61 - 273.15 = 327.46 \]Hence, the melting point of lead is \(327.46\, ^\circ C\).

Key concepts

Kelvin to Celsius

Temperature conversion from Kelvin to Celsius is a fundamental concept in understanding scientific temperature scales. When converting from Kelvin to Celsius, the key formula used is simple: subtract 273.15 from the Kelvin temperature. This formula arises because the Kelvin scale is based on absolute zero, the point where all molecular motion ceases.
In contrast, the Celsius scale is based on the freezing and boiling points of water, with 0°C being the freezing point. So, using the conversion, we can easily translate temperatures like those of substances with extremely high or low boiling or melting points from Kelvin to Celsius. This conversion helps us better relate the temperature to everyday experiences and scientific phenomena.

Boiling Point

The boiling point of a substance is the temperature at which it changes from a liquid to a gas. This occurs when the vapor pressure of the liquid equals the pressure surrounding the liquid.
Different substances have vastly different boiling points, indicating how diverse physical properties can be.

• For example, water boils at 100°C (373 K), but liquid nitrogen boils at 77 K (-196.15°C).
• The boiling points provide insight into the molecular forces within a substance.

Boiling points are crucial for understanding chemical processes, industrial applications, and even cooking. Knowing these points, especially in different temperature scales, helps scientists and engineers in various applications such as refrigeration and manufacturing.

Melting Point

The melting point of a substance is the temperature at which it changes from a solid to a liquid. This occurs when the solid's inter-molecular forces are overcome. Like boiling points, melting points vary widely among different materials

• For example, lead melts at 600.61 K, equivalent to 327.46°C.
• Water's melting point, for comparison, is 0°C (273.15 K).

The melting point is essential in determining a material's physical properties and suitability for specific uses. It is also a critical indicator in identifying substances and understanding their purity. This knowledge is utilized in fields like metallurgy, materials science, and geophysics.

Liquid Nitrogen

Liquid nitrogen is widely used in scientific research and industry due to its extremely low boiling point of 77 K, equivalent to -196.15°C. In its liquid form, nitrogen maintains temperatures well below freezing, which makes it ideal for cryogenic applications.
Examples include:

• Preserving biological specimens in cryogenics.
• Quick-freezing foods in the culinary industry.
• Providing cooling for superconductors in physics experiments.

The very low temperatures of liquid nitrogen make it a valuable resource for studying material behaviors at cryogenic temperatures. It is also used in medical and industrial fields for processes that require rapid cooling.

Liquid Helium

Liquid helium is even colder than liquid nitrogen, with a boiling point of 4.22 K (-268.93°C). This property makes it unique as it is the coldest known liquid, commonly used as a coolant in scientific experiments, especially those involving superconductivity.
Applications of liquid helium include:

• Coolant for MRI machines where extreme cold is essential.
• Used in research related to quantum mechanics.
• Cooling in large hadron colliders where superconducting magnets are operating.

Because of its incredibly low boiling point, it is indispensable where extremely low temperatures are required. Its usage is critical in unlocking mysteries about particle physics and quantum phenomena.

Lead

Lead is a heavy, malleable metal with a relatively low melting point of 600.61 K (327.46°C). This makes it easier to handle and shape in various applications, unlike metals with higher melting points.
Lead is used in:

• Batteries, especially those used in automobiles.
• Radiation shielding, due to its dense nature.
• Fishing weights and ballast keels for ships.

Understanding the melting point of lead is important in industries such as construction and manufacturing, where forming and shaping the metal is necessary. Lead's properties, including its softness and resistance to corrosion, make it ideal for certain niche applications, although care must be taken due to its toxicity.