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(a) In 1964 , the temperature in the Siberian village of Oymyakon reached \(-71^{\circ} \mathrm{C}\). What temperature is this on the Fahrenheit scale? (b) The highest officially recorded temperature in the continental United States was \(134^{\circ} \mathrm{F}\) in Death Valley, California. What is this temperature on the Celsius scale?

Short Answer

Expert verified
(a) -95.8°F, (b) 56.7°C.

Step by step solution

01

Understanding Temperature Conversion

To solve these problems, we need to use the formula for converting between Celsius and Fahrenheit. The formula to convert Celsius (C) to Fahrenheit (F) is:\[ F = \frac{9}{5}C + 32 \] and to convert Fahrenheit (F) to Celsius (C) is:\[ C = \frac{5}{9}(F - 32) \].
02

Convert -71^{\circ} C to Fahrenheit

We need to convert -71^{\circ} C to Fahrenheit using the formula \( F = \frac{9}{5}C + 32 \).Substitute \( C = -71 \):\[ F = \frac{9}{5}(-71) + 32 \]= \[ -127.8 + 32 \]= \[ -95.8^{\circ} \text{F} \].
03

Convert 134^{\circ} F to Celsius

Now, we will convert 134^{\circ} F to Celsius using the formula \( C = \frac{5}{9}(F - 32) \).Substitute \( F = 134 \):\[ C = \frac{5}{9}(134 - 32) \]= \[ \frac{5}{9}(102) \]= \[ 56.7^{\circ} \text{C} \].

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Key Concepts

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

Celsius to Fahrenheit conversion
Converting temperatures from Celsius to Fahrenheit is a handy skill to have. Whether you're traveling, cooking, or just interested in weather patterns, understanding this conversion can be incredibly useful. The formula to convert a temperature from Celsius (C) to Fahrenheit (F) is:

\[ F = \frac{9}{5}C + 32 \]

This formula works by first multiplying the Celsius temperature by 9/5, which is a factor used to adjust for the different scales of the two units. Then, 32 is added to adjust the freezing point difference between the two scales. For example, to convert the Siberian village temperature from -71^{\circ} \text{C} to Fahrenheit, we apply the formula:
  • Multiply -71 by 9/5, giving -127.8.
  • Add 32, resulting in -95.8^{\circ} \text{F}.
This process shows how even sub-zero temperatures can be accurately converted between systems, maintaining consistency in measurement across different scales.
Fahrenheit to Celsius conversion
Understanding how to convert Fahrenheit to Celsius is equally important, especially in regions where Fahrenheit is predominantly used. The conversion formula is quite straightforward:

\[ C = \frac{5}{9}(F - 32) \]

This formula works by subtracting 32 from the Fahrenheit temperature, which accounts for the difference in freezing points between the two scales, and then multiplying the result by 5/9 to adjust for unit scale difference. To convert the Death Valley temperature of 134^{\circ} \text{F} to Celsius, follow these steps:
  • Subtract 32 from 134 to get 102.
  • Multiply 102 by 5/9, resulting in 56.7^{\circ} \text{C}.
The process of conversion demonstrates how different weather conditions are expressed in a more universal manner, making temperature comprehension easier no matter what scale you're accustomed to.
Temperature scales
Temperature scales are fundamental to understanding how temperature is measured and compared globally. The Celsius scale was developed by Anders Celsius and is often used by most of the world for scientific and international purposes. On the Celsius scale, water freezes at 0°C and boils at 100°C under standard atmospheric conditions.

In contrast, the Fahrenheit scale, developed by Daniel Gabriel Fahrenheit, is primarily used in the United States for everyday temperature expression. On this scale, water freezes at 32°F and boils at 212°F. The key difference lies in their reference points and the size of each degree.

  • The Celsius scale is based on a metric system, with each degree representing 1/100 of the temperature change between the freezing and boiling points of water.
  • Fahrenheit, however, divides this range into 180 degrees, providing a greater precision often preferred for daily use in certain regions.
Understanding these scales allows us to better appreciate and interpret global weather conditions and scientific data. Knowing how to convert between the scales ensures clear communication in both casual and technical settings.

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Most popular questions from this chapter

An aluminum-alloy rod has a length of \(10.000 \mathrm{~cm}\) at \(20.000^{\circ} \mathrm{C}\) and a length of \(10.015 \mathrm{~cm}\) at the boiling point of water. (a) What is the length of the rod at the freezing point of water? (b) What is the temperature if the length of the rod is \(10.009 \mathrm{~cm} ?\)

One way to keep the contents of a garage from becoming too cold on a night when a severe subfreezing temperature is forecast is to put a tub of water in the garage. If the mass of the water is \(125 \mathrm{~kg}\) and its initial temperature is \(20^{\circ} \mathrm{C},\) (a) how much energy must the water transfer to its surroundings in order to freeze completely and (b) what is the lowest possible temperature of the water and its surroundings until that happens?

At what temperature is the Fahrenheit scale reading equal to (a) twice that of the Celsius scale and (b) half that of the Celsius scale?

A rectangular plate of glass initially has the dimensions \(0.200 \mathrm{~m}\) by \(0.300 \mathrm{~m}\). The coefficient of linear expansion for the glass is \(9.00 \times 10^{-6} / \mathrm{K} .\) What is the change in the plate's area if its temperature is increased by \(20.0 \mathrm{~K} ?\)

On finding your stove out of order, you decide to boil the water for a cup of tea by shaking it in a thermos flask. Suppose that you use tap water at \(19^{\circ} \mathrm{C},\) the water falls \(32 \mathrm{~cm}\) each shake, and you make 27 shakes each minute. Neglecting any loss of thermal energy by the flask, how long (in minutes) must you shake the flask until the water reaches \(100^{\circ} \mathrm{C} ?\)

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