Problem 7 - University Physics with Modern Physics

Question

(a) You feel sick and are told that you have a temperature of \(40.2^{\circ} \mathrm{C}\) . What is your temperature in "F? Should you be concerned? (b) The morning weather report in Sydney gives a current temperature of \(12^{\circ} \mathrm{C}\) . What is this temperature in \(^{\circ} \mathrm{F} ?\)

Step-by-Step Solution

Answer

(a) 104.36°F, yes, you should be concerned. (b) 53.6°F.

Step 1: Formula for Celsius to Fahrenheit

To convert a temperature in Celsius (C°) to Fahrenheit (F°), we use the formula:\[ F = \frac{9}{5}C + 32 \] where \( C \) is the temperature in Celsius.

Step 2: Convert 40.2°C to Fahrenheit

Using the conversion formula, substitute \( C = 40.2 \):\[ F = \frac{9}{5} \times 40.2 + 32 \]\[ F = 72.36 + 32 \]\[ F = 104.36^{\circ}F \]This means your temperature is 104.36°F.

Step 3: Evaluate if Concerned

A body temperature of 104.36°F is unusually high as the average body temperature in Fahrenheit is around 98.6°F, and a high fever is typically considered to be 100.4°F or higher. Therefore, you should be concerned and consider seeking medical attention.

Step 4: Convert 12°C to Fahrenheit

Using the same formula, replace \( C = 12 \):\[ F = \frac{9}{5} \times 12 + 32 \]\[ F = 21.6 + 32 \]\[ F = 53.6^{\circ}F \]Thus, the morning temperature in Sydney is 53.6°F.

Key Concepts

Celsius to Fahrenheit

Understanding how to convert temperatures from Celsius to Fahrenheit is essential, especially if you are in a region that uses Fahrenheit as the primary measurement of temperature. The formula to convert Celsius to Fahrenheit is:\[ F = \frac{9}{5}C + 32 \]where \( C \) is the temperature in Celsius and \( F \) is the temperature in Fahrenheit. This formula essentially scales the Celsius temperature by multiplying it by \( \frac{9}{5} \), a factor that accounts for the difference between the two scales. You then add 32, which aligns the freezing points of water between the scales. Let’s take an example from the exercise: if we have a temperature of 40.2°C, we substitute \( C = 40.2 \) into the formula:\[ F = \frac{9}{5} \times 40.2 + 32 \]First, multiply 40.2 by \( \frac{9}{5} \), which gives 72.36. Then, add 32 to get 104.36°F.Similarly, for a temperature of 12°C, the conversion would result in 53.6°F. This conversion is valuable because it helps interpret weather forecasts and personal temperatures correctly.

Fever Evaluation

Evaluating whether a fever is present is crucial for health and diagnosing potential illnesses. In Fahrenheit, the average body temperature is approximately 98.6°F. It is important to note the thresholds for fever, which typically starts at around 100.4°F. - Fever is a body's natural response and occurs when the body's temperature control is modified. - It could be due to infections, immune responses, or even environmental changes. In the exercise, we converted a temperature of 40.2°C to 104.36°F. According to medical standards, this temperature indicates a high fever. A high fever might lead to discomfort and potential complications, which is why it is concerning. It's advisable to seek medical attention because it could indicate a serious condition or require specific treatments.

Weather Temperature

Weather temperature readings are commonly given in Celsius or Fahrenheit, depending on the country or region. Understanding both can help to interpret and compare temperatures more accurately. In the exercise, the weather report indicated a temperature of 12°C in Sydney. By converting this to Fahrenheit using the steps earlier discussed, we calculate it as 53.6°F. This information: - Helps in planning daily activities. For instance, 12°C (or 53.6°F) might imply wearing a light jacket. - Allows for better communication, especially in international contexts where different scales are used. Being informed about how to convert these temperatures ensures you understand your environment better, no matter where you are.