Question

Express the following Celsius temperatures in degrees Fahrenheit: (a) \(19^{\circ} \mathrm{C}\) (b) \(-175^{\circ} \mathrm{C}\)

Short answer

(a) 66.2°F, (b) -283°F

Step-by-step solution

Understand the Formula

To convert Celsius (6 C") temperatures to Fahrenheit (6 F"), use the formula: \( F = \frac{9}{5} C + 32 \). This means you multiply the Celsius temperature by \( \frac{9}{5} \) and then add 32 to the result.

Convert 19°C to Fahrenheit

Use the conversion formula for (a) \( 19^{\circ} C \):\[F = \frac{9}{5} \times 19 + 32\]Calculate:\[F = 34.2 + 32 = 66.2^{\circ} F\]

Convert -175°C to Fahrenheit

Use the conversion formula for (b) \( -175^{\circ} C \):\[F = \frac{9}{5} \times (-175) + 32\]Calculate:\[F = -315 + 32 = -283^{\circ} F\]

Verify Your Results

Ensure both calculations use the correct formula and arithmetic has been done accurately for both conversions to achieve:(a) \( 66.2^{\circ} F \)(b) \( -283^{\circ} F \).

Key concepts

Celsius to Fahrenheit conversion

When we need to convert temperature from Celsius to Fahrenheit, we rely on a specific mathematical formula. This formula is essential for understanding how temperature scales compare and operate differently. The fundamental formula for converting Celsius to Fahrenheit is given by:\[ F = \frac{9}{5} C + 32 \]This formula is simple yet powerful. It involves two main steps:

• First, multiply the Celsius temperature by \( \frac{9}{5} \). This fraction represents the ratio between the size of the Fahrenheit and Celsius scales.
• Next, add 32 to the result. This is necessary because the freezing point of water differs between the scales; it is 0 degrees for Celsius but 32 degrees for Fahrenheit.

Understanding this formula makes it easier to switch between the two temperature scales, allowing us to communicate and interpret temperature data universally.

Fahrenheit temperature calculation

Calculating the temperature in Fahrenheit using a given Celsius value requires careful application of the conversion formula. Let's break it down using a practical example:Suppose you have a Celsius temperature of \( 19^{\circ} C \), and you need to find its Fahrenheit equivalent. Applying the formula to this will involve:

• First, multiply the Celsius value \( 19 \) by \( \frac{9}{5} \) which equals \( 34.2 \).
• Then, add 32 to \( 34.2 \), giving you \( 66.2^{\circ} F \).

This shows that the temperature of \( 19^{\circ} C \) converts to \( 66.2^{\circ} F \). Ensuring accuracy by rechecking your math can prevent mistakes in more complex scenarios.

Celsius temperature calculation

To calculate the Celsius equivalent from a Fahrenheit temperature, we rearrange and reverse the conversion process. While the original exercise focused on converting into Fahrenheit, sometimes the reverse calculation is necessary:For converting from Fahrenheit to Celsius, use the formula:\[ C = \frac{5}{9} (F - 32) \]In this formula:

• Subtract 32 from the Fahrenheit temperature. This adjustment aligns the freezing points of the scales.
• Multiply the result by \( \frac{5}{9} \) to convert the temperature difference proportional to the size differences in the scale units.

This process allows you to find the Celsius equivalent, ensuring a comprehensive understanding of both temperature scales and enhancing your ability to transition between them effortlessly.