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Chapter 2: Problem 60

The average temperature at the top of Jupiter's clouds is \(-244^{\circ} \mathrm{F}\). What is this temperature in \({ }^{\circ} \mathrm{C}\) ?

Short Answer

Expert verified
-153.33°C

Step by step solution

01

Identify the Conversion Formula

To convert Fahrenheit to Celsius, use the formula: \[°C = (°F - 32) \times \frac{5}{9}\]
02

Substitute the Given Temperature

Substitute the given temperature \(-244^{\circ}F\) into the conversion formula: \[°C = (-244 - 32) \times \frac{5}{9}\]
03

Simplify Inside the Parentheses

Subtract 32 from -244: \(-244 - 32 = -276\). The expression now is: \[°C = -276 \times \frac{5}{9}\]
04

Multiply and Simplify

Multiply -276 by \(\frac{5}{9}\): \(-276 \times \frac{5}{9} = -153.33\)
05

Write the Final Answer

The temperature in Celsius is \(-153.33^{\circ} \mathrm{C}\)

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Key Concepts

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

Fahrenheit to Celsius conversion
Understanding how to convert temperatures from Fahrenheit to Celsius is essential for many science and math problems. The formula to do this conversion is straightforward: \(°C = (°F - 32) \times \frac{5}{9}\). This formula shows that you first subtract 32 from the Fahrenheit temperature. After getting this result, multiply it by \(\frac{5}{9}\). This multiplication adjusts for the differences in the size of the degree units between Fahrenheit and Celsius scales. Knowing this formula can make it easier to switch between these two widely used temperature scales.
temperature scales
There are different temperature scales used around the world. The Fahrenheit scale, for example, is primarily used in the United States. Water freezes at 32°F and boils at 212°F under standard atmospheric pressure. On the other hand, the Celsius scale, also known as the Centigrade scale, is used in most other countries. In this scale, water freezes at 0°C and boils at 100°C.
By understanding both scales, it becomes easier to interpret temperatures in various contexts. Different fields like meteorology, cooking, and technology may use different scales, so knowing how to convert between them is very handy.
mathematical operations
To convert temperatures, you need to perform several mathematical operations. Let's break down what happens in each step of the Fahrenheit to Celsius conversion:
  • First, you perform subtraction: \(-244 - 32 = -276\)
  • Next, you’ll engage in multiplication: \(-276 \times \frac{5}{9}\)
  • Finally, you get the result: \(-153.33\)

Understanding how to handle basic math skills like subtraction and multiplication is critical. It allows you to solve more complex problems with ease. Practicing these operations can provide a strong arithmetic foundation for tackling various real-world and academic problems.

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Most popular questions from this chapter

A jewelry maker sells lots of sterling silver hearts with a mass of \(35.0 \mathrm{~g}\). Sterling silver is composed of \(92.5 \%\) silver and \(7.50 \%\) copper. (a) Write out the dimensional analysis factors that can be derived from the two percentages given above. Be sure to include units. (b) If the jeweler buys \(50.0\) lb of silver to make the hearts, how many sterling silver hearts can the jeweler make?

How many days would it take for a crepe myrtle tree to grow 1 \(\mathrm{cm}\) in height if it grows \(3.38\) feet per year? (Report your answer to three significant figures)

U.S. quarters are composed of \(91.67 \%\) copper and \(8.33 \%\) nickel. The mass of a quarter is \(5.670 \mathrm{~g}\). (a) Write out the dimensional analysis factors that can be derived from the two percentages given above. Be sure to include units. (b) If the U.S. mint buys \(3.0\) tons of copper for making quarters, how many quarters can it make?

Jodi, a sculptor, has prepared a mold for casting a bronze figure. The figure has a volume of \(225 \mathrm{~mL}\). If bronze has a density of \(7.8 \mathrm{~g} / \mathrm{mL}\) and Jodi likes to use \(90.0 \%\) of the bronze melted (she sometimes spills), how many ounces of bronze does Jodi need to melt in the preparation of the bronze figure?

In a role-playing video game (RPG) your character is a Human Paladin that can carry \(115 \mathrm{lb}\) of gear. Your character is carrying 92 lb of gear and a vial of strength potion (which allows you to carry an additional \(50.0\) lb of gear). If you find a cave filled with mass potions (used for resisting strong winds), after using the strength potion, how many vials can you collect if the vials each contain \(50.0 \mathrm{~mL}\) of mass potion with a density of \(193 \mathrm{~g} / \mathrm{mL}\) ? The vials have negligible mass.
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