Question

Body temperature on the average is \(98.6^{\circ} \mathrm{F}\). What is this on (a) the Celsius scale and (b) the Kelvin scale?

Short answer

(a) The given temperature on the Celsius scale is \(37^{\circ} \mathrm{C}\). (b) The given temperature on the Kelvin scale is \(310.15 K\).

Step-by-step solution

Convert Fahrenheit to Celsius

First, we need to convert the given temperature from Fahrenheit to Celsius using the formula: \[ C = \frac{5}{9}(F - 32) \] Plugging the given temperature into the formula, we get: \[ C = \frac{5}{9}(98.6 - 32) \]

Calculate the Celsius Temperature

Now, calculate the Celsius temperature. Perform the calculations inside the parentheses first, and then multiply by the fraction: \[ C = \frac{5}{9}(66.6) \] \[ C = 37^{\circ} \mathrm{C} \] So, the given temperature in Celsius is \(37^{\circ} \mathrm{C}\).

Convert Celsius to Kelvin

Now, we need to convert the Celsius temperature to Kelvin using the formula: \[ K = C + 273.15 \] Plugging the calculated Celsius temperature into the formula, we get: \[ K = 37 + 273.15 \]

Calculate the Kelvin Temperature

Finally, calculate the Kelvin temperature. Add the Celsius temperature to the constant (273.15): \[ K = 310.15 \] So, the given temperature in Kelvin is \(310.15 K\).

Final Answer:

We have now converted the given temperature into both Celsius and Kelvin scales: (a) The given temperature on the Celsius scale is \(37^{\circ} \mathrm{C}\). (b) The given temperature on the Kelvin scale is \(310.15 K\).

Key concepts

Fahrenheit to Celsius

Understanding the conversion from Fahrenheit to Celsius is crucial, as these are the most commonly used temperature scales in daily life and in various fields. The formula for this conversion is quite simple:

\( C = \frac{5}{9}(F - 32) \)

In this equation, \(C\) represents the Celsius temperature, \(F\) is the Fahrenheit temperature, and the fraction \(\frac{5}{9}\) is the ratio of Celsius to Fahrenheit degree increments. So, if you're given a temperature of \(98.6^\circ F\) (a typical human body temperature), you subtract 32 from it, which leaves you with 66.6. Multiply that number by \(\frac{5}{9}\), and you get \(37^\circ C\). This conversion is useful for not only understanding weather forecasts in different regions but also in scientific contexts where Celsius is predominantly used.

Real-Life Application

In practical terms, if you are traveling, cooking, or engaged in science experiments, converting Fahrenheit to Celsius allows you to follow instructions and understand information that is presented in the other scale.

• Traveling: Different countries use different scales, so knowing how to convert temperatures is useful when adapting to new climates.
• Cooking: Recipes often list oven temperatures in Fahrenheit or Celsius, so conversion skills are handy for culinary success.
• Science: Celsius is a common scale in science, making it necessary to convert Fahrenheit temperatures to Celsius for consistency in experiments.

Celsius to Kelvin

The conversion from Celsius to Kelvin is a critical process in the scientific community where absolute temperature measurements are required, such as in the fields of physics and chemistry. Unlike Celsius and Fahrenheit, which set their zero points at easily reproducible temperature points related to the properties of water, the Kelvin scale is an absolute temperature scale. It starts at absolute zero, the theoretical lowest possible temperature.

To convert Celsius to Kelvin, you simply add 273.15 to the Celsius temperature:
\( K = C + 273.15 \)

For instance, if the Celsius temperature is \(37^\circ C\), adding 273.15 gives you 310.15 K. It's important to note that, unlike Celsius and Fahrenheit, there are no negative numbers on the Kelvin scale because it starts from the lowest limit of temperature.

Scientific Importance

Understanding Kelvin is especially important in scientific research and applications that deal with thermodynamics and properties of gases, among others.

• Physics: In thermal physics, the Kelvin scale is key in discussions of theoretical principles and laws.
• Chemistry: Chemical reactions often require precise temperature control, where Kelvin is the standard.
• Astronomy: The temperatures of stars and other celestial bodies are typically expressed in Kelvin.

Temperature Scales

Temperature scales provide a consistent way to measure heat energy. The three main temperature scales used around the world are Fahrenheit, Celsius, and Kelvin. Each scale has its own applications and conversion formulas allowing interconnectivity.

The Fahrenheit scale is often used in the United States for weather and cooking. In most other countries, the Celsius scale is preferred for these purposes. The main difference between the two is the point at which each scale is defined: Fahrenheit uses the freezing and boiling points of brine, while Celsius uses the freezing and boiling points of water.

Meanwhile, the Kelvin scale is the temperature metric used internationally in the scientific community because of its thermodynamic consistency. It is an absolute scale with its zero point at absolute zero, the point where molecular energy is at a minimum.

Universal Understanding

Knowing how to read and convert between these scales is a necessary skill to navigate a variety of disciplines and everyday situations.

• International Communication: With multiple scales used globally, conversions are essential for communication and collaboration.
• Education: Understanding various scales is part of the fundamental science curriculum.
• Technology: Many scientific instruments and technologies incorporate these temperature measurements, so knowing the scales makes using such equipment more intuitive.