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What’s your normal body temperature? It may not be 98.6 \(^{\circ} \mathrm{F}\), the often-quoted average that was determined in the nineteenth century. A more recent study has reported an average temperature of 98.2 \(^{\circ} \mathrm{F}\). What is the difference between these averages, expressed in Celsius degrees?

Short Answer

Expert verified
The difference is 0.2°C.

Step by step solution

01

Convert Fahrenheit to Celsius

The formula to convert Fahrenheit to Celsius is \(C = \frac{5}{9}(F - 32)\). First, convert 98.6 \(^{\circ} \mathrm{F}\) by substituting \(F = 98.6\) into the formula: \[C = \frac{5}{9}(98.6 - 32)\].
02

Calculate Celsius for 98.6°F

Now calculate \( C = \frac{5}{9}(98.6 - 32) = \frac{5}{9} \times 66.6 \approx 37.0^{\circ} \mathrm{C}\).
03

Convert Second Temperature to Celsius

Use the same formula for 98.2 \(^{\circ} \mathrm{F}\): \(C = \frac{5}{9}(98.2 - 32)\).
04

Calculate Celsius for 98.2°F

Calculate \(C = \frac{5}{9}(98.2 - 32) = \frac{5}{9} \times 66.2 \approx 36.8^{\circ} \mathrm{C}\).
05

Find the Difference in Celsius

The difference between the two temperatures in Celsius is \(37.0^{\circ} \mathrm{C} - 36.8^{\circ} \mathrm{C} = 0.2^{\circ} \mathrm{C}\).

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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 an essential skill, especially when comparing different measurement systems. When converting Celsius to Fahrenheit, one uses the equation:
\[ F = \frac{9}{5}C + 32 \]This equation tells us that we start by multiplying the Celsius temperature by 9, divide by 5 (this part scales the temperature), and finally, add 32 to shift the scale from Celsius to Fahrenheit.
  • Example: To convert 37°C, typically considered a normal body temperature in Celsius, follow these steps:
  • Multiply 37 by 9, which gives 333.
  • Then divide 333 by 5, resulting in 66.6.
  • Adding 32 gives you 98.6°F, which is the standard average body temperature in Fahrenheit.
This formula helps us appreciate how different temperatures correlate between these scales. By knowing this conversion, one can seamlessly switch between Celsius and Fahrenheit according to the need.
Temperature Difference
Calculating temperature differences in Celsius becomes straightforward once the temperatures in Fahrenheit are converted.
The key is to remember that differences in temperature will be the same magnitude regardless of the scale used—Fahrenheit or Celsius—due to the linearity of the conversion formula.
In the exercise, when both 98.6°F and 98.2°F are converted into Celsius, we get 37.0°C and 36.8°C, respectively.
  • This means the difference in Celsius is simply 37.0°C minus 36.8°C.
  • This results in a temperature difference of 0.2°C.
The process demonstrates how converting and calculating differences in temperatures is a practical application of the conversion formula. Once numbers are in the same units, subtraction gives an accurate difference in temperature values.
Body Temperature
The concept of body temperature is pivotal for understanding human health. Typically represented as 98.6°F, this number is often seen as the benchmark for normal body temperature, though science recognizes variability.
More contemporary studies suggest a slight shift in this average, indicating 98.2°F as the potential new norm. Understanding these temperatures in Celsius is convenient:
  • 98.6°F converts to approximately 37.0°C.
  • 98.2°F converts to around 36.8°C.
These minor variations are small in magnitude but can be significant in interpreting body health conditions or variations.
Awareness of body temperature helps in tracking health and wellness. Knowing how to quickly convert and understand these numbers can be crucial in daily health assessments and understanding medical information across different regions of the world.

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Most popular questions from this chapter

ssm At a fabrication plant, a hot metal forging has a mass of 75 \({kg}\) and a specific heat capacity of 430 \({J} / {kg} \cdot {C}^{\circ}\) . To harden it, the forging is immersed in 710 \({kg}\) of oil that has a temperature of \(32^{\circ} {C}\) and a specific heat capacity of 2700 \({J} / {kg} \cdot {C}^{\circ}\) ). The final temperature of the oil and forging at thermal equilibrium is \(47^{\circ} {C}\) . Assuming that heat flows only between the forging and the oil, determine the initial temperature of the forging.

When it rains, water vapor in the air condenses into liquid water, and energy is released. (a) How much energy is released when 0.0254 m (one inch) of rain falls over an area of \(2.59 \times 10^{6} {m}^{2}\) (one square mile)? (b) If the average energy needed to heat one home for a year is \(1.50 \times 10^{11} {J}\) , how many homes could be heated for a year with the energy determined in part (a)?

Occasionally, huge icebergs are found floating on the ocean's currents. Suppose one such iceberg is 120 \({km}\) long, 35 \({km}\) wide, and 230 \({m}\) thick. (a) How much heat would be required to melt this iceberg (assumed to be at \(0^{\circ} {C}\) ) into liquid water at \(0^{\circ} {C}\) ? The density of ice is 917 \({kg} / {m}^{3} .\) (b) The annual energy consumption by the United States is about \(1.1 \times 10^{20} {J}\) . If this energy were delivered to the iceberg every year, how many years would it take before the ice melted?

(a) Objects A and B have the same mass of 3.0 kg. They melt when \(3.0 \times 10^{4} {J}\) of heat is added to object \({A}\) and when \(9.0 \times 10^{4} {J}\) is added to object B. Determine the latent heat of fusion for the substance from which each object is made. (b) Find the heat required to melt object A when its mass is 6.0 kg.

ssm An unknown material has a normal melting/freezing point of \(-25.0^{\circ} {C},\) and the liquid phase has a specific heat capacity of 160 \({J} / {kg} \cdot {C}^{\circ}\) . One-tenth of a kilogram of the solid at \(-25.0^{\circ} {C}\) is put into a 0.150 \({-kg}\) aluminum calorimeter cup that contains 0.100 \({kg}\) of glycerin. The temperature of the cup and the glycerin is initially \(27.0^{\circ} {C}\) . All the unknown material melts, and the final temperature at equilibrium is \(20.0^{\circ} {C}\) . The calorimeter neither loses energy to nor gains energy from the external environment. What is the latent heat of fusion of the unknown material?

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