/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 66 The temperature in a freezer is ... [FREE SOLUTION] | 91Ó°ÊÓ

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The temperature in a freezer is set at \(30^{\circ} \mathrm{F}\). What is this temperature on the Celsius scale?

Short Answer

Expert verified
The temperature is approximately -1.11°C on the Celsius scale.

Step by step solution

01

Recall the Conversion Formula

To convert a temperature from Fahrenheit to Celsius, use the following formula: \[ C = \frac{5}{9} imes (F - 32) \]where \( C \) is the temperature in Celsius and \( F \) is the temperature in Fahrenheit.
02

Substitute the Given Temperature

Substitute \( F = 30 \) into the conversion formula:\[ C = \frac{5}{9} imes (30 - 32) \]
03

Perform the Operations Inside the Parentheses

Calculate \( 30 - 32 \):\[ 30 - 32 = -2 \]Substitute this result back into the formula:\[ C = \frac{5}{9} imes (-2) \]
04

Multiply and Simplify

Perform the multiplication:\[ C = \frac{5}{9} imes (-2) = \frac{-10}{9} \approx -1.11 \]Thus, when rounded to two decimal places, the temperature in Celsius is approximately \( -1.11^{ ext{°C}} \).

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Key Concepts

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

Fahrenheit to Celsius conversion
The conversion from Fahrenheit to Celsius is vital in temperature calculations, especially if you're dealing with different systems of measurement. The process is pretty straightforward, thanks to a standard formula. To convert a temperature from Fahrenheit to Celsius, use the equation: \[ C = \frac{5}{9} \times (F - 32) \] Here, *C* stands for the temperature in Celsius, and *F* represents the temperature in Fahrenheit. By following this formula, you can accurately change any Fahrenheit temperature into its Celsius equivalent. For example, if you have a temperature of 30°F and want to convert it, you'd follow these steps:
  • First, find the difference: 30 - 32 = -2.
  • Next, multiply this number by \( \frac{5}{9} \): \( \frac{5}{9} \times (-2) = \frac{-10}{9} \).
  • Finally, simplify and round if necessary, which gives approximately -1.11°C.
This method is essential in many scientific and day-to-day scenarios where temperature needs to be calculated or understood in a different measurement system.
Celsius scale
The Celsius scale is a crucial part of understanding temperature and is widely used across the globe. It was introduced by Swedish astronomer Anders Celsius in the early 18th century. This scale is based on the properties of water; it defines 0°C as the freezing point of water and 100°C as the boiling point under standard atmospheric pressure. One of the primary benefits of the Celsius scale is its ease of use compared to other scales, such as Fahrenheit, especially within scientific communities and most countries. Understanding how this scale operates and its relation to the natural states of water makes it easier to comprehend various natural and laboratory environments where temperature plays a key role.
Temperature calculations
Temperature calculations are an everyday task in multiple fields, including science, cooking, and weather forecasting. These calculations often involve converting temperatures from one scale to another or finding temperature differences. To ensure precision, make sure you follow correct mathematical procedures and utilize calculators when necessary. Key Points for Accurate Temperature Calculations:
  • Double-check the conversion formulas used, especially when working between Fahrenheit and Celsius.
  • Be consistent with decimal points and rounding to avoid errors.
  • Be aware that temperature can affect the outcome in chemistry experiments, cooking, or any process that depends on precise thermal control.
Getting comfortable with temperature calculations allows for a clearer understanding and more effective results in both academic and practical situations.

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Most popular questions from this chapter

Big ldea What do we call energy that is transferred because of a temperature difference?

A large punch bowl holds \(3.99 \mathrm{~kg}\) of lemonade (which is essentially water) at \(20.5^{\circ} \mathrm{C} . \mathrm{A} 0.0550-\mathrm{kg}\) ice cube at \(-10.2{ }^{\circ} \mathrm{C}\) is placed in the lemonade. What is the final temperature of the system and the amount of ice (if any) remaining? Ignore any heat exchange with the bowl or the surroundings.

A system consists of a \(0.130-\mathrm{kg}\) chunk of ice floating in \(1.12 \mathrm{~kg}\) of water, all at \(0{ }^{\circ} \mathrm{C}\). How much thermal energy must be added to the system to convert it to \(1.25 \mathrm{~kg}\) of water at \(15.0^{\circ} \mathrm{C}\) ?

The lowest temperature ever recorded on Earth was set at Vostok, Antarctica, on July 21, 1983. The temperature on that day fell to \(-89.2{ }^{\circ} \mathrm{C}\), well below the temperature of dry ice. What is this temperature in degrees Fahrenheit?

PA brass plate has a circular hole whose diameter is slightly smaller than the diameter of an aluminum ball. (a) If the ball and the plate are always kept at the same temperature, should the temperature of the system be increased or decreased in order for the ball to fit through the hole? (b) Choose the best explanation from among the following: A. The aluminum ball changes its diameter more with temperature than the brass plate changes its dimensions, and therefore the temperature should be decreased. B. Changing the temperature won't change the fact that the ball is larger than the hole. C. Heating the brass plate makes its hole larger, which will allow the ball to pass through.

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