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Convert the following Celsius temperatures to Fahrenheit: (a) \(-62.8^{\circ} \mathrm{C}\), the lowest temperature ever recorded in North America (February \(3,1947,\) Snag, Yukon); (b) \(56.7^{\circ} \mathrm{C},\) the highest temperature ever recorded in the United States (July \(10,1913,\) Death Valley, California); (c) \(31.1^{\circ} \mathrm{C},\) the world's highest average annual temperature (Lugh Ferrandi, Somalia).

Short Answer

Expert verified
The Fahrenheit equivalents of the given temperatures are: (a) -81.04℉ (b) 134.06℉ (c) 87.98℉

Step by step solution

01

Convert -62.8 Celsius to Fahrenheit

To convert -62.8 degrees Celsius to Fahrenheit, apply the formula: \( F = (9/5) × (-62.8) + 32 \). Solve the multiplication first, then add 32. This gives the Fahrenheit equivalent of -62.8 degrees Celsius.
02

Convert 56.7 Celsius to Fahrenheit

Similarly, to convert 56.7 degrees Celsius to Fahrenheit, apply the same formula: \( F = (9/5) × 56.7 + 32 \). Again, solve the multiplication first, then add 32. This gives the Fahrenheit equivalent of 56.7 degrees Celsius.
03

Convert 31.1 Celsius to Fahrenheit

Finally, to convert 31.1 degrees Celsius to Fahrenheit, use the formula: \( F = (9/5) × 31.1 + 32 \). Solve the multiplication first, then add 32. This gives the Fahrenheit equivalent of 31.1 degrees Celsius.

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Key Concepts

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

Celsius to Fahrenheit Conversion
The process of converting temperatures from Celsius to Fahrenheit revolves around a simple mathematical equation. This formula is critical for transforming the Celsius scale, commonly used across the globe, into the Fahrenheit scale, which is primarily used in the United States. The conversion formula is:
  • \( F = \left(\frac{9}{5} \times C\right) + 32 \)
Here, \( C \) represents the temperature in Celsius, and \( F \) represents the temperature in Fahrenheit.
To apply this formula, simply multiply the Celsius temperature by \( \frac{9}{5} \) and then add 32. This two-step process helps translate the metric temperature into a format familiar for those in Fahrenheit-using regions.
For example, to convert -62.8°C, you calculate:
  • Multiply: \( \frac{9}{5} \times (-62.8) = -113.04 \)
  • Add 32: \( -113.04 + 32 = -81.04°F \)
It's essential to follow these steps carefully to ensure the correct temperature reading.
Understanding Temperature Measurement
Temperature is a fundamental measurement in meteorology, climatology, and physics. It signifies how hot or cold an object or environment is, relative to an established scale. Typically, there are two primary scales for measurement: Celsius and Fahrenheit.
The Celsius scale is prevalent worldwide, especially in scientific contexts and is part of the metric system. It is based on the freezing and boiling points of water, defined as 0°C and 100°C respectively. Meanwhile, the Fahrenheit scale uses 32°F as the freezing point of water and 212°F as the boiling point.
These scales were developed to provide a uniform way to compare temperatures. They allow us to understand everyday phenomena such as weather conditions, cooking temperatures, and even physical reactions. Each scale has its own unique applications, enabling diverse use in different regions and settings.
The Importance of Temperature in Physics Education
In the field of physics education, temperature plays a crucial role in understanding various phenomena and principles. It is a measure of thermal energy and influences how we perceive heat, cold, and energy transfer.
In physics, temperature is often part of experiments involving thermodynamics, where students learn about heat transfer, energy conservation, and the laws of thermodynamics. For students, comprehending how temperature is measured and converted is fundamental to grasp more complex scientific concepts.
  • It helps explain the behavior of gases – as temperature rises, gases expand.
  • It aids in understanding the states of matter – solids, liquids, and gases – and how they change with varying temperatures.
  • Temperature differences drive interesting studies in heat engines, which are pivotal for understanding energy conversions and efficiencies.
By learning about temperature measurement and conversion, students gain a foundational skill important for broader scientific exploration and research.

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Most popular questions from this chapter

A industrious explorer of the polar regions has devised a contraption for melting ice. It consists of a sealed \(10 \mathrm{~L}\) cylindrical tank with a porous grate separating the top half from the bottom half. The bottom half includes a paddle wheel attached to an axle that passes outside the cylinder, where it is attached by a gearbox and pulley system to a stationary bicycle. Pedaling the bicycle rotates the paddle wheel inside the cylinder. The tank includes \(6.00 \mathrm{~L}\) of water and \(3.00 \mathrm{~kg}\) of ice at \(0.0^{\circ} \mathrm{C}\). The water fills the bottom chamber, where it may be agitated by the paddle wheel, and partially fills the upper chamber, which also includes the ice. The bicycle is pedaled with an average torque of \(25.0 \mathrm{~N} \cdot \mathrm{m}\) at a rate of 30.0 revolutions per minute. The system is \(70 \%\) efficient. (a) For what length of time must the explorer pedal the bicycle to melt all the ice? (b) How much longer must he pedal to raise the temperature of the water to \(10.5^{\circ} \mathrm{C}\) ?

In an effort to stay awake for an all-night study session, a student makes a cup of coffee by first placing a \(200 \mathrm{~W}\) electric immersion heater in \(0.320 \mathrm{~kg}\) of water. (a) How much heat must be added to the water to raise its temperature from \(20.0^{\circ} \mathrm{C}\) to \(80.0^{\circ} \mathrm{C} ?\) (b) How much time is required? Assume that all of the heater's power goes into heating the water.

A laboratory technician drops a \(0.0850 \mathrm{~kg}\) sample of unknown solid material, at \(100.0^{\circ} \mathrm{C}\), into a calorimeter. The calorimeter can, initially at \(19.0^{\circ} \mathrm{C},\) is made of \(0.150 \mathrm{~kg}\) of copper and contains \(0.200 \mathrm{~kg}\) of water. The final temperature of the calorimeter can and contents is \(26.1^{\circ} \mathrm{C}\). Compute the specific heat of the sample.

You are making pesto for your pasta and have a cylindrical measuring cup \(10.0 \mathrm{~cm}\) high made of ordinary glass \(\left[\beta=2.7 \times 10^{-5}\left(\mathrm{C}^{\circ}\right)^{-1}\right]\) that is filled with olive oil \(\left[\beta=6.8 \times 10^{-4}\left(\mathrm{C}^{\circ}\right)^{-1}\right]\) to a height of \(3.00 \mathrm{~mm}\) below the top of the cup. Initially, the cup and oil are at room temperature \(\left(22.0^{\circ} \mathrm{C}\right)\). You get a phone call and forget about the olive oil, which you inadvertently leave on the hot stove. The cup and oil heat up slowly and have a common temperature. At what temperature will the olive oil start to spill out of the cup?

You have \(750 \mathrm{~g}\) of water at \(10.0^{\circ} \mathrm{C}\) in a large insulated beaker. How much boiling water at \(100.0^{\circ} \mathrm{C}\) must you add to this beaker so that the final temperature of the mixture will be \(75^{\circ} \mathrm{C}\) ?

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