Question

The boiling point of liquid nitrogen, used in the removal of warts and in other surgical applications, is \(-195.8{ }^{\circ} \mathrm{C}\). What is this temperature in kelvins and in degrees Fahrenheit?

Short answer

77.35 K, -320.44 °F

Step-by-step solution

Convert to Kelvin

To convert the temperature from Celsius to Kelvin, use the formula: \( K = °C + 273.15 \). Substituting the given Celsius temperature: \( K = -195.8 + 273.15 \). Calculate the value to find the Kelvin temperature.

Calculate Kelvin Temperature

Perform the calculation: \( K = -195.8 + 273.15 = 77.35 \). Thus, the temperature in Kelvin is 77.35 K.

Convert to Fahrenheit

To convert the temperature from Celsius to Fahrenheit, use the formula: \( °F = \left( °C \times \frac{9}{5} \right) + 32 \). Substitute the given Celsius temperature: \( °F = \left( -195.8 \times \frac{9}{5} \right) + 32 \).

Calculate Fahrenheit Temperature

Perform the calculation: \( °F = \left( -195.8 \times 1.8 \right) + 32 = -352.44 + 32 = -320.44 \). Thus, the temperature in Fahrenheit is -320.44 °F.

Key concepts

Celsius to Kelvin

The Celsius and Kelvin scales are crucial temperature measurements in science. They both measure temperatures based on the molecular energy in substances.
To convert a temperature from Celsius to Kelvin, a simple formula is used: add 273.15 to the Celsius temperature.
This works because 0 Kelvin, or absolute zero, is the theoretical point where molecular motion stops completely.

• Formula: \( K = °C + 273.15 \)
• Example: Convert -195.8 °C to Kelvin.

When you plug the Celsius temperature into this formula, \( K = -195.8 + 273.15 \), you get 77.35 K.
This conversion is straightforward because the scale sizes are the same. This means an increase of one Celsius degree is equivalent to an increase of one Kelvin. Understanding this conversion is vital for scientific calculations where Kelvin may be the preferred unit.

Celsius to Fahrenheit

When converting temperatures from Celsius to Fahrenheit, the formula is slightly more complex than converting to Kelvin. This is because the Fahrenheit scale is based on a different zero point and step size than the Celsius scale.
The conversion involves multiplying the Celsius temperature by 9/5 and then adding 32.

• Formula: \( °F = \left( °C \times \frac{9}{5} \right) + 32 \)
• Example: Convert -195.8 °C to Fahrenheit.

The calculation for -195.8 °C is: \( °F = \left( -195.8 \times \frac{9}{5} \right) + 32 = -320.44 °F \).
Understanding these differences and the formula helps in accurately converting and communicating temperatures in these two systems. The Fahrenheit scale, while less commonly used in scientific contexts, is still widely used in countries like the United States and among historians of older scientific literature.

Boiling Point of Nitrogen

Nitrogen is a common element in our atmosphere and has practical applications in its liquid form. One of its key properties is its boiling point, which is the temperature at which it changes from a liquid to a gas.
This property is essential for its use in various scientific and industrial fields, such as cryogenics and medicine.

• Boiling point in Celsius: -195.8 °C
• Boiling point in Kelvin: 77.35 K
• Boiling point in Fahrenheit: -320.44 °F

These values show how extreme the boiling point is compared to common environmental temperatures, highlighting the necessity of low temperatures in its storage and use.
Understanding the boiling point across different scales allows for safe handling and precise applications of liquid nitrogen in diverse settings. Liquid nitrogen's extreme cold makes it useful in preserving biological samples and performing certain medical procedures, among other uses.