Problem 11 - University Physics with Modern Physics

Question

Why. Liquid nitrogen is a relatively inexpensive material that is often used to perform entertaining low-temperature physics demonstrations. Nitrogen gas liquefies at a temperature of \(-346^{\circ} \mathrm{F}\) . Convert this temperature to (a) \(^{\circ} \mathrm{C}\) and \((\mathrm{b}) \mathrm{K}\) .

Step-by-Step Solution

Answer

The liquid nitrogen temperature is approximately -210°C and 63.15 K.

Step 1: Understand the Conversion Formula From Fahrenheit to Celsius

To convert a temperature from Fahrenheit to Celsius, use the formula: \[ C = \frac{5}{9}(F - 32) \]where \( C \) is the temperature in Celsius and \( F \) is the temperature in Fahrenheit.

Step 2: Apply the Conversion Formula to Find Temperature in Celsius

Given the temperature of liquid nitrogen as \(-346^{\circ} \mathrm{F}\), substitute \( F = -346 \) into the conversion formula:\[C = \frac{5}{9}(-346 - 32)\]Calculate the expression inside the parentheses:\[-346 - 32 = -378\]Now, substitute back:\[C = \frac{5}{9}(-378)\]Calculate the Celsius temperature:\[C \approx -210^{\circ} \mathrm{C}\]

Step 3: Understand the Conversion Formula From Celsius to Kelvin

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

Step 4: Apply the Conversion Formula to Find Temperature in Kelvin

Using the Celsius temperature found in Step 2, which is \(-210^{\circ} \mathrm{C}\), substitute into the Kelvin conversion formula:\[K = -210 + 273.15\]Calculate the Kelvin temperature:\[K \approx 63.15 \mathrm{K}\]

Key Concepts

Fahrenheit to Celsius

When you want to convert a temperature from Fahrenheit to Celsius, you need to use the formula: \( C = \frac{5}{9}(F - 32) \), where \( C \) stands for Celsius and \( F \) stands for Fahrenheit. This formula helps adjust for the difference in the starting point and interval size of the two scales. Fahrenheit places its zero point at \(32^{\circ}\), while Celsius sets its zero at the freezing point of water. So, first subtract \(32\) from the Fahrenheit value to align the zero point with Celsius. Then, multiply by \(\frac{5}{9}\) to adjust the scale interval size, as there are \(180\) Fahrenheit intervals between water's freezing and boiling points, compared to \(100\) in Celsius. To find the temperature of liquid nitrogen, which is \(-346^{\circ} \mathrm{F}\), compute:

• Subtract \(32\) from \(-346\) resulting in \(-378\).
• Then, multiply \(-378\) by \(\frac{5}{9}\), which gives approximately \(-210^{\circ} \mathrm{C}\).

Celsius to Kelvin

The Celsius to Kelvin conversion is straightforward as it involves adding or subtracting a constant number: \( K = C + 273.15 \). This formula reflects the offset between the zero points of the two scales. Celsius is based on the freezing point of water, while Kelvin begins at absolute zero, the point where all molecular motion ceases. Hence, every temperature in Celsius simply shifts upwards by \(273.15\) to convert to Kelvin. Using our earlier result of liquid nitrogen being \(-210^{\circ} \mathrm{C}\), convert to Kelvin by calculating:

• Add \(273.15\) to \(-210\) to find approximately \(63.15 \text{ K}\).

Kelvin does not use the degree symbol, simplifying notation and emphasizing its use in scientific calculations.

Liquid Nitrogen

Liquid nitrogen is nitrogen in a liquid state at an extremely low temperature. It's often used for demonstrations due to its fascinating and dramatic properties when in contact with everyday materials. The temperature at which nitrogen becomes liquid is about \(-346^{\circ} \mathrm{F}\) or \(-210^{\circ} \mathrm{C}\) or \(63.15 \mathrm{K}\). At this point, its low temperature can cause materials to become extremely brittle. Some compelling uses of liquid nitrogen you might come across include:

• Instant freezing of food, which preserves texture and flavor better than slower freezing methods.
• Creating fog effects for theatrical productions to simulate chilled environments.
• In medicine, to destroy unhealthy tissue such as in cryosurgery.

Liquid nitrogen provides a practical showcase of thermodynamic principles and presents a tangible connection to temperature scales, helping learners to grasp complex thermal concepts more easily.