Question

The highest recorded body temperature that a person has survived is \(46.5^{\circ} \mathrm{C}\). Calculate that temperature in degrees Fahrenheit and in kelvins.

Short answer

46.5°C is equal to 115.7°F and 319.65 K.

Step-by-step solution

- Convert Celsius to Fahrenheit

Use the formula to convert Celsius to Fahrenheit: \[ F = \frac{9}{5}C + 32 \] Plug in \( 46.5 \) degrees Celsius: \[ F = \frac{9}{5}(46.5) + 32 \] Simplify the expression: \[ F = 83.7 + 32 = 115.7 \] So, \( 46.5^{\bullet}\text{C} \) is equal to \( 115.7^{\bullet}\text{F} \).

- Convert Celsius to Kelvin

Use the formula to convert Celsius to Kelvin: \[ K = C + 273.15 \] Plug in \( 46.5 \) degrees Celsius: \[ K = 46.5 + 273.15 \] Simplify the expression: \[ K = 319.65 \] So, \( 46.5^{\bullet}\text{C} \) is equal to \( 319.65 \text{K} \).

Key concepts

Celsius to Fahrenheit

When converting temperatures from Celsius to Fahrenheit, we use a formula based on the relationship between these two scales. The formula is: \[ F = \frac{9}{5}C + 32 \] Here, \( F \) represents degrees Fahrenheit and \( C \) represents degrees Celsius. This equation indicates that you multiply the Celsius temperature by \( \frac{9}{5} \), and then add 32 to the result. Let's break it down: - Start by multiplying the Celsius value (\( 46.5 \)) by 9. - Next, divide that product by 5, resulting in \( 83.7 \). - Finally, add 32 to \( 83.7 \), giving you \( 115.7 \) degrees Fahrenheit. Understanding this formula can be quite useful in contexts where temperatures need to be quickly converted, such as weather predictions or medical scenarios.

Celsius to Kelvin

To convert Celsius to Kelvin, we use a simpler formula due to the direct relationship between these two scales. The formula is: \[ K = C + 273.15 \] In this case, \( K \) stands for Kelvin and \( C \) stands for Celsius. This formula is straightforward because the Kelvin scale is an absolute temperature scale starting at absolute zero (-273.15 degrees Celsius), so: - To convert \( 46.5 \) degrees Celsius to Kelvin, you simply add \( 273.15 \) to the Celsius value. - Adding these, \( 46.5 + 273.15 = 319.65 \), giving our result as \( 319.65 \) Kelvin. The Kelvin scale is extensively used in scientific experiments and studies, particularly in the fields of physics and chemistry.

thermodynamics

Thermodynamics is the branch of physics that deals with the relationships between heat and other forms of energy. It describes how thermal energy is converted to and from other forms of energy and how it affects matter. Thermodynamics involves several key concepts that are crucial in understanding temperature conversions: - **First Law of Thermodynamics**: This defines the principle of conservation of energy, stating that energy cannot be created or destroyed, but it can change forms. - **Second Law of Thermodynamics**: This law introduces the concept of entropy, stating that in any energy exchange, if no energy enters or leaves the system, the potential energy of the state will always be less than that of the initial state. Thermodynamics is essential in many scientific and engineering fields, helping us understand everything from engines to biological systems. Conversion of temperature scales like Celsius to Kelvin directly ties into thermodynamics as it helps scientists measure and manage thermal energy more accurately.