Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

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

Short Answer

Expert verified
-62.8°C = -81.04°F; 56.7°C = 134.06°F; 31.1°C = 87.98°F.

Step by step solution

01

Understand the Conversion Formula

The formula for converting Celsius (C) to Fahrenheit (F) is \( F = \frac{9}{5} \times C + 32 \). This formula ensures that we correctly convert any temperature from the Celsius scale to the Fahrenheit scale by considering both scales’ differences in temperature unit and zero point offset.
02

Convert -62.8°C to Fahrenheit

Substitute \( C = -62.8 \) into the formula: \[ F = \frac{9}{5} \times (-62.8) + 32 \].Calculate \(\frac{9}{5} \times (-62.8) = -113.04 \) then add 32: \( F = -113.04 + 32 = -81.04 \).Thus, -62.8°C is equivalent to -81.04°F.
03

Convert 56.7°C to Fahrenheit

Substitute \( C = 56.7 \) into the formula: \[ F = \frac{9}{5} \times 56.7 + 32 \].Calculate \(\frac{9}{5} \times 56.7 = 102.06 \), then add 32:\( F = 102.06 + 32 = 134.06 \).Thus, 56.7°C is equivalent to 134.06°F.
04

Convert 31.1°C to Fahrenheit

Substitute \( C = 31.1 \) into the formula:\[ F = \frac{9}{5} \times 31.1 + 32 \].Calculate \(\frac{9}{5} \times 31.1 = 55.98 \) then add 32:\( F = 55.98 + 32 = 87.98 \).Thus, 31.1°C is equivalent to 87.98°F.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

Key Concepts

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

Temperature Conversion
Temperature conversion is a fundamental concept in understanding the different ways we measure heat. The Celsius and Fahrenheit scales are two of the most commonly used systems. To convert a temperature from Celsius to Fahrenheit, we use a specific formula. This formula is:
  • Fahrenheit (\( F \)) = \( \frac{9}{5} \) \( \times \) Celsius (\( C \)) + 32
This formula works because it accounts for both the size of the temperature units and their starting points. On the Celsius scale, the freezing point of water is 0 degrees, while on the Fahrenheit scale, it’s 32 degrees.
By adjusting for these differences, the formula ensures accurate temperature conversion between the two scales.When applying this formula to any temperature given in Celsius, you simply multiply the Celsius value by \( \frac{9}{5} \) and then add 32 to your result. This simple conversion is used in meteorology, science, and everyday life to communicate temperature information effectively.'
Fahrenheit Scale
The Fahrenheit scale is one of the most widely recognized temperature scales, particularly in the United States. It was developed by Daniel Gabriel Fahrenheit in the early 18th century. Unlike the Celsius scale, where temperatures are based around the freezing and boiling points of water, the Fahrenheit system was originally based on an older method of measuring temperatures derived from the temperature of mixed ice and water.
The scale defines the freezing point of water as 32 degrees Fahrenheit and the boiling point as 212 degrees Fahrenheit. This scale offers finer granularity compared to Celsius, which is why some people prefer it for daily weather reports. In essence, a one-degree change on the Celsius scale equates to a 1.8-degree change on the Fahrenheit scale. This difference is what makes the conversion formula so essential in understanding how to switch between these units.
  • Common in the US and Caribbean
  • Used mainly in meteorology and everyday temperature readings
Celsius Scale
Named after the Swedish astronomer Anders Celsius, the Celsius scale is a metric system temperature scale used around the world. Its significance lies in its scientific basis and ease of use when it comes to daily temperature measurements. The key reference points of the Celsius scale are 0 degrees as the freezing point of water and 100 degrees as the boiling point.
One of the main advantages of this scale is its simplicity in terms of scientific measurement, supporting an intuitive understanding of everyday temperatures. Unlike the Fahrenheit scale, Celsius is part of the International System of Units (SI), making it the standard in most countries globally. It simplifies temperature-related calculations and conversions, being largely compatible with the Kelvin scale, another SI temperature scale used in scientific contexts.
  • Commonly used in science
  • Part of the metric system
  • Globally preferred, except in the USA and a few other countries

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A technician measures the specific heat of an unidentified liquid by immersing an electrical resistor in it. Electrical energy is converted to heat transferred to the liquid for 120 s at a constant rate of 65.0 W. The mass of the liquid is 0.780 kg, and its temperature increases from 18.55\(^\circ\)C to 22.54\(^\circ\)C. (a) Find the average specific heat of the liquid in this temperature range. Assume that negligible heat is transferred to the container that holds the liquid and that no heat is lost to the surroundings. (b) Suppose that in this experiment heat transfer from the liquid to the container or surroundings cannot be ignored. Is the result calculated in part (a) an overestimate or an underestimate of the average specific heat? Explain.

CP A person of mass 70.0 kg is sitting in the bathtub. The bathtub is 190.0 cm by 80.0 cm; before the person got in, the water was 24.0 cm deep. The water is at 37.0\(^\circ\)C. Suppose that the water were to cool down spontaneously to form ice at 0.0\(^\circ\)C, and that all the energy released was used to launch the hapless bather vertically into the air. How high would the bather go? (As you will see in Chapter 20, this event is allowed by energy conservation but is prohibited by the second law of thermodynamics.)

The hot glowing surfaces of stars emit energy in the form of electromagnetic radiation. It is a good approximation to assume e = 1 for these surfaces. Find the radii of the following stars (assumed to be spherical): (a) Rigel, the bright blue star in the constellation Orion, which radiates energy at a rate of \(2.7 \times 10{^3}{^2} W\) and has surface temperature 11,000 K; (b) Procyon B (visible only using a telescope), which radiates energy at a rate of \(2.1 \times 10{^2}{^3} W\) and has surface temperature 10,000 K. (c) Compare your answers to the radius of the earth, the radius of the sun, and the distance between the earth and the sun. (Rigel is an example of a supergiant star, and Procyon B is an example of a white dwarf star.)

Like the Kelvin scale, the Rankine scale is an absolute temperature scale: Absolute zero is zero degrees Rankine (0\(^\circ\)R). However, the units of this scale are the same size as those of the Fahrenheit scale rather than the Celsius scale. What is the numerical value of the triple-point temperature of water on the Rankine scale?

A metal sphere with radius 3.20 cm is suspended in a large metal box with interior walls that are maintained at 30.0\(^\circ\)C. A small electric heater is embedded in the sphere. Heat energy must be supplied to the sphere at the rate of 0.660 J/s to maintain the sphere at a constant temperature of 41.0\(^\circ\)C. (a) What is the emissivity of the metal sphere? (b) What power input to the sphere is required to maintain it at 82.0\(^\circ\)C? What is the ratio of the power required for 82.0\(^\circ\)C to the power required for 41.0\(^\circ\)C? How does this ratio compare with 2\(^4\)? Explain.

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free