Problem 1 - College Physics

Question

\(\bullet\) (a) While vacationing in Europe, you feel sick and are told that you have a temperature of \(40.2^{\circ} \mathrm{C}\) . Should you be concerned? What is your temperature in \(^{\circ} \mathrm{F} ?\) (b) The morning weather report in Sydney predicts a high temperature of \(12^{\circ} \mathrm{C}\) . Will you need to bring a jacket? What is this temperature in \(^{\circ} \mathrm{F} ?(\mathrm{c})\) A friend has suggested that you go swimming in a pool having water of temperature 350 \(\mathrm{K}\) . Is this safe to do? What would this temperature be on the Fahrenheit and Celsius scales?

Step-by-Step Solution

Answer

(a) 104.36°F indicates a fever. (b) 53.6°F requires a jacket. (c) 350 K is dangerously hot at 170.33°F.

Step 1: Convert Celsius to Fahrenheit for part (a)

To convert Celsius to Fahrenheit, use the formula: \[ F = \left( \frac{9}{5} \times C \right) + 32 \]Given that your temperature is 40.2°C:\[ F = \left( \frac{9}{5} \times 40.2 \right) + 32 \]\[ F = 72.36 + 32 \]\[ F = 104.36^{\circ} \mathrm{F} \]Since a normal body temperature is around 98.6°F, a temperature of 104.36°F indicates a fever, and you should be concerned.

Step 2: Convert Celsius to Fahrenheit for part (b)

Use the same conversion formula for the morning temperature in Sydney:\[ F = \left( \frac{9}{5} \times 12 \right) + 32 \]\[ F = 21.6 + 32 \]\[ F = 53.6^{\circ} \mathrm{F} \]Since 53.6°F is quite cool, you will likely need a jacket.

Step 3: Convert Kelvin to Celsius for part (c)

First, convert the temperature from Kelvin to Celsius using the formula:\[ C = K - 273.15 \]Given the water temperature is 350 K:\[ C = 350 - 273.15 \]\[ C = 76.85^{\circ} \mathrm{C} \]Since typical swimming pool temperatures are around 25°C to 28°C, 76.85°C is dangerously hot.

Step 4: Convert Celsius to Fahrenheit for the pool temperature

Now convert 76.85°C (from Kelvin conversion) to Fahrenheit:\[ F = \left( \frac{9}{5} \times 76.85 \right) + 32 \]\[ F = 138.33 + 32 \]\[ F = 170.33^{\circ} \mathrm{F} \]This temperature is extremely hot for swimming, and it is not safe.

Key Concepts

Celsius to Fahrenheit

Converting temperatures from Celsius to Fahrenheit is often necessary when traveling or dealing with information shared in different regions of the world. The formula to convert Celsius (C) to Fahrenheit (F) is: \[ F = \left( \frac{9}{5} \times C \right) + 32 \].

• To use this formula, first multiply the Celsius temperature by \(\frac{9}{5}\).
• Next, add 32 to the result to obtain the Fahrenheit temperature.

For example, a temperature recorded as 12°C in Sydney translates to 53.6°F based on this calculation.

Knowing this conversion is crucial, especially when assessing temperatures like 40.2°C, which equals 104.36°F and signifies a fever since normal body temperature is about 98.6°F.

Kelvin to Celsius

The Kelvin to Celsius conversion is straightforward, as both scales increment at the same rate. To make the conversion, you simply need to subtract273.15from the Kelvin temperature. The formula is: \[ C = K - 273.15 \].

• This conversion is essential in scientific settings where Kelvin is commonly used.
• By subtracting 273.15, you translate temperatures into the more familiar Celsius scale.

For instance, a water temperature of 350 Kelvin converts to 76.85°C.

Such a high temperature indicates it is much too hot for safe swimming. Generally, swimming pools maintain a temperature between 25°C and 28°C, making this conversion especially pertinent for safety assessments.

Temperature Safety

Understanding temperature safety is important for assessing the risk of certain weather conditions or environments. When temperatures fall outside safe ranges, they can pose a threat to health and safety.

• Body temperatures above 98.6°F (37°C) may indicate fever or illness.
• Environmental temperatures like a pool at 76.85°C are extremely dangerous and unsuitable for activities.

Awareness of appropriate and safe temperature ranges is critical in both daily activities and for health monitoring.

When the temperature is predicted to be 12°C (53.6°F), it's advisable to prepare for cooler weather, such as bringing a jacket if going out.

Fever Recognition

Recognizing fever is crucial for early illness detection and response. A fever typically sets in when the body temperature surpasses 100.4°F (38°C), indicating the body's response to infection.

• Measured in Fahrenheit, a fever starts around 100.4°F.
• A temperature of 104°F, like 40.2°C when converted, is an indicator of a significant fever.

Understanding how different temperatures are classified and how to convert them is essential for managing health effectively.

Recognizing the signs of fever allows for timely medical consultation and appropriate measures to be taken to address any underlying health issues.