Question

Convert the following temperatures to degrees Celsius or Fahrenheit: (a) \(95^{\circ} \mathrm{F}\), the temperature on a hot summer day; (b) \(12^{\circ} \mathrm{F}\), the temperature on a cold winter day; (c) a \(102^{\circ} \mathrm{F}\) fever; (d) a furnace operating at \(1852^{\circ} \mathrm{F} ;\) (e) \(-273.15^{\circ} \mathrm{C}\) (theoretically the lowest attainable temperature).

Short answer

(a) 35°C, (b) -11.11°C, (c) 38.89°C, (d) 1000°C, (e) -459.67°F.

Step-by-step solution

Understand the Conversion Formulas

To convert Celsius to Fahrenheit, use the formula \( F = \frac{9}{5}C + 32 \). To convert Fahrenheit to Celsius, use the formula \( C = \frac{5}{9}(F - 32) \). These formulas help us transform temperatures from one scale to another.

Convert 95°F to Celsius

Use the formula for converting Fahrenheit to Celsius: \[ C = \frac{5}{9}(95 - 32) \] First, subtract 32 from 95, which gives 63. Then multiply 63 by \( \frac{5}{9} \). The result is 35°C, which is the equivalent temperature in Celsius.

Convert 12°F to Celsius

Using the same conversion formula: \[ C = \frac{5}{9}(12 - 32) \] First, subtract 32 from 12 to get -20. Next, multiply -20 by \( \frac{5}{9} \) to get approximately -11.11°C.

Convert 102°F to Celsius

Again using the formula: \[ C = \frac{5}{9}(102 - 32) \] Subtract 32 from 102 to get 70. Multiply 70 by \( \frac{5}{9} \), resulting in approximately 38.89°C.

Convert 1852°F to Celsius

Use the conversion formula: \[ C = \frac{5}{9}(1852 - 32) \] Subtract 32 from 1852 to obtain 1820. Multiply 1820 by \( \frac{5}{9} \), which gives 1000°C, the Celsius equivalent.

Convert -273.15°C to Fahrenheit

Utilize the formula for Celsius to Fahrenheit conversion: \[ F = \frac{9}{5}(-273.15) + 32 \] First, multiply -273.15 by \( \frac{9}{5} \) resulting in -491.67. Then, add 32 to get -459.67°F.

Key concepts

Celsius to Fahrenheit

The Celsius to Fahrenheit conversion is an essential part of understanding how temperature scales relate to each other. This process involves taking a temperature value in Celsius and converting it to its equivalent in Fahrenheit. The formula used for this conversion is: \( F = \frac{9}{5}C + 32 \). Here is how it works:

• Multiply the Celsius temperature by \( \frac{9}{5} \).
• Add 32 to the result to convert the temperature to Fahrenheit.

This formula is based on the relationship between the freezing and boiling points of water in both temperature scales. Water freezes at 0°C, which is 32°F, and boils at 100°C, which is 212°F. Knowing how to perform this conversion is very handy, especially when reading weather reports or cooking recipes that use different temperature scales.

Fahrenheit to Celsius

Converting Fahrenheit to Celsius can help you understand temperatures in contexts you're more familiar with, especially if you're used to the metric system. The formula to convert a temperature from Fahrenheit to Celsius is: \( C = \frac{5}{9}(F - 32) \).Let’s explain the steps:

• Subtract 32 from the Fahrenheit temperature. This adjusts the temperature based on the difference in zero points between the two scales.
• Multiply the result by \( \frac{5}{9} \). This scales down the temperature difference to Celsius units.

By using this conversion, you can easily adjust the temperature readings when participating in activities where Celsius is the standard, like traveling to countries that use the metric system or engaging in scientific studies.

Temperature Scales

Temperature scales serve as a way to measure and express thermal energy, and they spring from different historical and scientific backgrounds. The main scales include Celsius, Fahrenheit, and Kelvin.

• Celsius: Used predominantly in most parts of the world, especially in scientific contexts, Celsius defines the freezing point of water at 0° and the boiling point at 100°.
• Fahrenheit: Used mainly in the United States, this scale sets the freezing point of water at 32° and the boiling point at 212°.
• Kelvin: Used primarily in scientific settings, this scale starts at absolute zero (-273.15°C) and uses the same increment size as Celsius.

Understanding temperature scales helps you interpret various temperature-related phenomena and allows for seamless conversion between scales as needed.

Conversion Formulas

Conversion formulas are mathematical expressions that allow us to switch between different temperature scales.

• For Celsius to Fahrenheit: Use \( F = \frac{9}{5}C + 32 \).
• For Fahrenheit to Celsius: Use \( C = \frac{5}{9}(F - 32) \).

These conversion formulas are essential tools for translating temperature readings from one scale to another. It's important to note that these conversions are linear, meaning that each degree change is consistent between scales. For example, a change of 10°C is equivalent to an 18°F change. By mastering these formulas, you can navigate between temperature scales with ease, using them for academic, culinary, and everyday purposes.