Question

Here are a few common temperatures on the Fahrenheit scale. Convert each of these to the Kelvin scale. a. \(95^{\circ} \mathrm{F}\left(\text { a hot day) } \text { b. } 350^{\circ} \mathrm{F} \text { (oven temperature) c. } 5^{\circ} \mathrm{F} \text { (freezer) }\right.\)

Short answer

95°F = 308.15 K, 350°F = 449.82 K, 5°F = 258.15 K.

Step-by-step solution

Understand the Conversion Formula

To convert Fahrenheit to Kelvin, you first need to convert Fahrenheit to Celsius and then Celsius to Kelvin. The formulas are as follows: 1. \[ C = \frac{5}{9}(F - 32) \]2. \[ K = C + 273.15 \]

Convert 95°F to Celsius

Use the formula \[ C = \frac{5}{9}(F - 32) \] to convert 95°F. Plug in the value: \[ C = \frac{5}{9}(95 - 32) = \frac{5}{9}(63) = 35°C \]

Convert Celsius to Kelvin for 95°F

Now convert 35°C to Kelvin. Use the formula: \[ K = C + 273.15 \] \[ K = 35 + 273.15 = 308.15 \text{ K} \]

Convert 350°F to Celsius

Again, use the Fahrenheit to Celsius formula: \[ C = \frac{5}{9}(350 - 32) = \frac{5}{9}(318) = 176.67°C \]

Convert Celsius to Kelvin for 350°F

Convert 176.67°C to Kelvin using the formula: \[ K = C + 273.15 \] \[ K = 176.67 + 273.15 = 449.82 \text{ K} \]

Convert 5°F to Celsius

Use the conversion formula for 5°F: \[ C = \frac{5}{9}(5 - 32) = \frac{5}{9}(-27) = -15°C \]

Convert Celsius to Kelvin for 5°F

Convert -15°C to Kelvin: \[ K = C + 273.15 \] \[ K = -15 + 273.15 = 258.15 \text{ K} \]

Key concepts

Fahrenheit to Kelvin conversion

Converting between different temperature scales may seem daunting at first, but it's just a matter of understanding the right formulas and steps. One common conversion task is converting Fahrenheit to Kelvin. To do this, you need a two-step process. First, convert the Fahrenheit temperature to Celsius, then convert the Celsius temperature to Kelvin.

Start with the formula to change Fahrenheit (°F) to Celsius (°C):

• \[ C = \frac{5}{9}(F - 32) \]

Take your result in Celsius and convert it to Kelvin (K) using:

• \[ K = C + 273.15 \]

This method works because the Kelvin scale is directly related to the Celsius scale, just shifted by 273.15 units. By following these steps, you can convert any Fahrenheit temperature into Kelvin smoothly.

Celsius conversion

Celsius, also known as centigrade, is one of the most commonly used scales for measuring temperature worldwide. Converting temperatures to and from the Celsius scale is essential in many scientific and everyday applications.

When you're converting from Celsius to other scales, you follow straightforward formulas:

• To Fahrenheit: \[ F = \frac{9}{5}C + 32 \]
• To Kelvin: \[ K = C + 273.15 \]

Celsius is based on the freezing and boiling points of water at 0°C and 100°C, respectively. This makes it an intuitive scale for many practical purposes.Conversely, when starting with temperatures in Fahrenheit, it's important to rearrange the conversion formulas to solve for Celsius, which simplifies the process of further conversion to Kelvin or any other regional scales that might be used.

thermodynamics concepts

In thermodynamics, temperature is a crucial parameter that influences system behavior and the flow of energy. Temperature conversions, like from Fahrenheit to Kelvin, are a vital part of handling and communicating thermal data, especially since different regions and scientific contexts may use varying temperature scales.

Thermodynamics emphasizes:

• The transfer of heat energy from one system to another.
• The changes of state that occur when sufficient energy is added or removed.

Understanding how to convert and reconcile different temperature units ensures accurate thermodynamic calculations, which are important in many fields such as engineering, meteorology, and cooking.

temperature scales

Temperature scales are systems for measuring how hot or cold an object is. There are several key temperature scales used around the world, each with its own basis and applications.

Fahrenheit is used primarily in the United States. Its defining points are the freezing point of water at 32°F and boiling at 212°F.

The Celsius scale, adopted in most of the world, sets the freezing and boiling points of water at 0°C and 100°C, respectively, making it straightforward for most scientific work.

Kelvin is the SI unit of temperature and is used in science to avoid negative temperatures. Its zero point, absolute zero, is theoretically the coldest possible temperature, where molecular motion is minimal. Knowing how these scales relate and convert between each other is critical for scientific calculations and global communication. It's what allows coherent data exchange between diverse regions and industries.