Question

Perform the indicated temperature conversions. a. \(25.1^{\circ} \mathrm{F}\) to \(^{\circ} \mathrm{C}\) b. \(25.1^{\circ} \mathrm{C}\) to \(^{\circ} \mathrm{F}\) c. \(25.1 \mathrm{K}\) to \(^{\circ} \mathrm{C}\) d. \(25.1 \mathrm{K}\) to \(^{\circ} \mathrm{F}\)

Short answer

a. \(-3.83^{\circ} \mathrm{C}\) b. \(77.18^{\circ} \mathrm{F}\) c. \(-248.05^{\circ} \mathrm{C}\) d. \(-414.89^{\circ} \mathrm{F}\)

Step-by-step solution

Use the Fahrenheit to Celsius_conversion formula

To convert the temperature from Fahrenheit to Celsius, we will use the formula: \(°C = \frac{°F - 32}{1.8}\)

Plug in the given temperature

Insert the given temperature of \(25.1° \mathrm{F}\) into the formula: \(°C = \frac{25.1 - 32}{1.8}\)

Calculate the result

Calculate the Celsius temperature: \(°C = \frac{-6.9}{1.8} \approx -3.83\) Therefore, \(25.1^{\circ} \mathrm{F}\) is approximately \(-3.83^{\circ} \mathrm{C}\). b. Convert \(25.1^{\circ} \mathrm{C}\) to \(^{\circ} \mathrm{F}\):

Use the Celsius to Fahrenheit_conversion formula

To convert the temperature from Celsius to Fahrenheit, we will use the formula: \(°F = °C * 1.8 + 32\)

Plug in the given temperature

Insert the given temperature of \(25.1^{\circ} \mathrm{C}\) into the formula: \(°F = 25.1 * 1.8 + 32\)

Calculate the result

Calculate the Fahrenheit temperature: \(°F = 45.18 + 32 = 77.18\) Therefore, \(25.1^{\circ} \mathrm{C}\) is approximately \(77.18^{\circ} \mathrm{F}\). c. Convert \(25.1 \mathrm{K}\) to \(^{\circ} \mathrm{C}\):

Use the Kelvin to Celsius_conversion formula

To convert the temperature from Kelvin to Celsius, we will use the formula: \(°C = K - 273.15\)

Plug in the given temperature

Insert the given temperature of \(25.1 \mathrm{K}\) into the formula: \(°C = 25.1 - 273.15\)

Calculate the result

Calculate the Celsius temperature: \(°C = -248.05\) Therefore, \(25.1 \mathrm{K}\) is approximately \(-248.05^{\circ} \mathrm{C}\). d. Convert \(25.1 \mathrm{K}\) to \(^{\circ} \mathrm{F}\):

Use the Kelvin to Fahrenheit_conversion formula

To convert the temperature from Kelvin to Fahrenheit, we will use the formula: \(°F = \frac{K * 9}{5} - 459.67\)

Plug in the given temperature

Insert the given temperature of \(25.1 \mathrm{K}\) into the formula: \(°F = \frac{25.1 * 9}{5} - 459.67\)

Calculate the result

Calculate the Fahrenheit temperature: \(°F = \frac{225.9}{5} - 459.67 \approx -414.89\) Therefore, \(25.1 \mathrm{K}\) is approximately \(-414.89^{\circ} \mathrm{F}\).

Key concepts

Fahrenheit to Celsius Conversion

When you need to convert a temperature from Fahrenheit to Celsius, it's important to understand the underlying formula: \(°C = \frac{°F - 32}{1.8}\).

This equation is derived from the freezing and boiling points of water: 32°F for freezing and 212°F for boiling, compared to 0°C for freezing and 100°C for boiling in the Celsius scale. The difference between these two sets of values is that the Celsius scale jumps in 100 increments while the Fahrenheit scale jumps in 180 increments for the same change in temperature, thus the factor of 1.8 (or \(\frac{9}{5}\)).

To make this more digestible, let's consider the following steps with an example:

• Subtract 32 from the Fahrenheit temperature.
• Divide the result by 1.8 to get the temperature in Celsius.

For instance, using the provided exercise, if you have a temperature of 25.1°F, first subtract 32 which gives you -6.9. Then, divide -6.9 by 1.8, yielding approximately -3.83°C, which is now a much more understandable value in the Celsius scale.

Celsius to Fahrenheit Conversion

Transforming a Celsius temperature to Fahrenheit is just as essential, especially when communicating with regions that use different temperature scales. The formula is straightforward: \(°F = °C * 1.8 + 32\).

This formula incorporates the factors needed to go from the 100-degree increment on the Celsius scale for water's phase change to the 180-degree increment on Fahrenheit's scale, while also adjusting for the different starting points of the two scales.

Lets break it down:

• Multiply the Celsius temperature by 1.8.
• Add 32 to the result to get the Fahrenheit temperature.

For a practical example, when converting 25.1°C, you multiply by 1.8 to get 45.18, then add 32 to end up with 77.18°F. Simple, right? This method ensures you can switch between scales without confusion.

Kelvin to Celsius Conversion

Conversion from Kelvin to Celsius touches on the absolute temperature scale, which is Kelvin. This conversion is vital in scientific contexts where Kelvin is predominantly used. The formula is direct: \(°C = K - 273.15\).

Did you know that the Kelvin scale starts at absolute zero, which is -273.15°C? That's the coldest possible temperature where all molecular motion stops. Therefore, converting Kelvin to Celsius means you're subtracting the absolute zero value from the Kelvin temperature.

Let's simplify it:

• Just subtract 273.15 from the Kelvin temperature to convert it to Celsius.

So, if you're starting with 25.1 K, once you subtract 273.15, you're left with -248.05°C, showing that 25.1 K is a temperature far below the freezing point of water.

Kelvin to Fahrenheit Conversion

When shifting from Kelvin to Fahrenheit, we once again take into account the zero point of the Fahrenheit scale and convert to a scale that's relatable for everyday use. The conversion formula is \(°F = \frac{K * 9}{5} - 459.67\).

This equation encompasses the conversion from Kelvin to Celsius and then from Celsius to Fahrenheit. Here’s how to digest easily:

• Multiply the Kelvin temperature by \(\frac{9}{5}\)
• Subtract 459.67 from the result to adjust for the Fahrenheit scale's lower freezing point.

Applying this to our case, starting with 25.1 K, you would multiply by \(\frac{9}{5}\) to get 45.18 and then subtract 459.67, resulting in -414.89°F. It shows how the Kelvin temperature relates to Fahrenheit, keeping in mind that the negative value indicates a temperature that is much colder than what we experience in everyday life.