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Chapter 17: Problem 3

(a) On January 22, 1943, the temperature in Spearfish, South Dakota, rose from -4.0\(^\circ\)F to 45.0\(^\circ\)F in just 2 minutes. What was the temperature change in Celsius degrees? (b) The temperature in Browning, Montana, was 44.0\(^\circ\)F on January 23, 1916. The next day the temperature plummeted to -56\(^\circ\)F. What was the temperature change in Celsius degrees?

Short Answer

Expert verified
(a) 27.22掳C, (b) -55.56掳C.

Step by step solution

01

Convert Fahrenheit to Celsius Formula

The formula to convert a temperature from Fahrenheit (F) to Celsius (C) is given by: \[ C = \frac{5}{9}(F - 32) \] We will use this formula to compute the temperature changes in Celsius for both parts (a) and (b).
02

Convert Initial and Final Temperatures for Part (a)

Calculate Celsius temperatures for initial and final values in part (a).- Initial temperature: \[ C_{initial} = \frac{5}{9}(-4 - 32) = \frac{5}{9}(-36) = -20 \] - Final temperature: \[ C_{final} = \frac{5}{9}(45 - 32) = \frac{5}{9}(13) \approx 7.22 \]
03

Calculate Temperature Change in Celsius for Part (a)

Subtract the initial Celsius temperature from the final Celsius temperature for part (a) to find the temperature change.\[ \Delta C = C_{final} - C_{initial} = 7.22 - (-20) = 7.22 + 20 \approx 27.22 \] Thus, the temperature change in Celsius is approximately 27.22掳C.
04

Convert Initial and Final Temperatures for Part (b)

Calculate Celsius temperatures for initial and final values in part (b).- Initial temperature: \[ C_{initial} = \frac{5}{9}(44 - 32) = \frac{5}{9}(12) \approx 6.67 \] - Final temperature: \[ C_{final} = \frac{5}{9}(-56 - 32) = \frac{5}{9}(-88) = -48.89 \]
05

Calculate Temperature Change in Celsius for Part (b)

Subtract the final Celsius temperature from the initial Celsius temperature for part (b) to determine the temperature change.\[ \Delta C = C_{final} - C_{initial} = -48.89 - 6.67 = -55.56 \] Thus, the temperature change in Celsius is approximately -55.56掳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
Temperature is often measured in either Fahrenheit or Celsius, and it's crucial to be able to convert between these two scales. The formula for converting Fahrenheit to Celsius is quite simple:
  • The formula is \( C = \frac{5}{9}(F - 32) \), where \( C \) represents Celsius and \( F \) represents Fahrenheit.
To convert a Fahrenheit temperature to Celsius, you simply subtract 32 from the Fahrenheit value and then multiply the result by \( \frac{5}{9} \). This method is commonly used in scientific calculations and everyday situations where temperature conversion is necessary.
Whether determining the weather outside or engineering a scientific experiment, understanding how to convert between Fahrenheit and Celsius will aid in comprehending temperature-related data presented in different formats.
Temperature change calculation
Understanding how to calculate temperature change is important in grasping weather fluctuations and their implications. This involves converting specific temperatures from Fahrenheit to Celsius and then finding the difference between the two values in Celsius.
  • Suppose you have an initial temperature \( C_{initial} \) and a final temperature \( C_{final} \).
  • The temperature change \( \Delta C \) is calculated as \( C_{final} - C_{initial} \).
In our example, temperatures initially measured in Fahrenheit are converted to Celsius using the formula discussed earlier. After obtaining the Celsius values, the change is found by simple subtraction.
This process is vital for recognizing the extent of temperature shifts, whether for academic purposes or evaluating historical weather anomalies.
Historical weather events
Historical weather events often provide insight into the extreme capabilities of Earth's climate. Events like the dramatic temperature changes recorded in Spearfish, South Dakota and Browning, Montana, highlight extreme weather phenomena that can occur.
  • For instance, in Spearfish on January 22, 1943, the temperature shot up by about \( 27.22\)掳C in just two minutes.
  • In another case, Browning experienced a sudden drop by approximately \(-55.56\)掳C overnight from January 23, 1916.
Understanding these events involves recognizing how quickly temperatures can change under specific atmospheric conditions.
Not only do these historical accounts serve as interesting case studies, but they also underscore the importance of accurate temperature conversion and weather monitoring in modern times.

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Most popular questions from this chapter

A 4.00-kg silver ingot is taken from a furnace, where its temperature is 750.0\(^\circ\)C, and placed on a large block of ice at 0.0\(^\circ\)C. Assuming that all the heat given up by the silver is used to melt the ice, how much ice is melted?

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.)

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.

An aluminum tea kettle with mass 1.10 kg and containing 1.80 kg of water is placed on a stove. If no heat is lost to the surroundings, how much heat must be added to raise the temperature from 20.0\(^\circ\)C to 85.0\(^\circ\)C?

A constant-volume gas thermometer registers an absolute pressure corresponding to 325 mm of mercury when in contact with water at the triple point. What pressure does it read when in contact with water at the normal boiling point?
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