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(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 \(^{\circ} \mathrm{F} ?\)

Short Answer

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

Step by step solution

01

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.
02

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.
03

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.
04

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.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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.

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Most popular questions from this chapter

A pot with a steel bottom 8.50 \(\mathrm{mm}\) thick rests on a hot stove.The area of the bottom of the pot is 0.150 \(\mathrm{m}^{2}\) . The water inside the pot is at \(100.0^{\circ} \mathrm{C},\) and 0.390 \(\mathrm{kg}\) are evaporated every 3.00 \(\mathrm{min}\) . Find the temperature of the lower surface of the pot, which is in contact with the stove.

Find the Celsius temperatures corresponding to (a) a winter night im Seattle \(\left(41.0^{\circ} \mathrm{F}\right) ;(\mathrm{b})\) a hot summer day in Palm Springs \(\left(107.0^{\circ} \mathrm{F}\right) ;(\mathrm{c})\) a cold winter day in northern Manitoba \(\left(-18.0^{\circ} \mathrm{F}\right)\) .

An insulated beaker with negligible mass contains 0.250 \(\mathrm{kg}\) of water at a temperature of \(75.0^{\circ} \mathrm{C}\) . How many kilograms of ice at a temperature of \(-20.0^{\circ} \mathrm{C}\) must be dropped into the water to make the final temperature of the system \(30.0^{\circ} \mathrm{C} ?\)

A copper calorimeter can with mass 0.446 kg contains 0.0950 \(\mathrm{kg}\) of ice. The system is initially at \(0.0^{\circ} \mathrm{C}\) (a) If 0.0350 \(\mathrm{kg}\) of steam at \(100.0^{\circ} \mathrm{C}\) and 1.00 atm pressure is added to the can, what is the final temperature of the calorimeter can and its contents? (b) At the final temperature, how many kilograms are there of ice, how many of liquid water, and how many of steam?

A crate of fruit with mass 35.0 \(\mathrm{kg}\) and specific heat 3650 \(\mathrm{J} / \mathrm{kg} \cdot \mathrm{K}\) slides down a ramp inclined at \(36.9^{\circ} \mathrm{C}\) below the horizontal. The ramp is 8.00 \(\mathrm{m}\) long. (a) If the crate was at rest at the top of the incline and has a speed of 2.50 \(\mathrm{m} / \mathrm{s}\) at the bottom, how much work was done on the crate by friction? (b) If an amount of heat equal to the magnitude of the work done by friction goes into the crate of fruit and the fruit reaches a uniform final temperature, what is its temperature change?

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