Problem 3 - University Physics with Modern Physics

Question

(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?

Step-by-Step Solution

Answer

(a) 27.22°C, (b) -55.56°C.

Step 1: 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).

Step 2: 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: \[ C_{final} = \frac{5}{9}(45 - 32) = \frac{5}{9}(13) \approx 7.22 \]

Step 3: 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°C.

Step 4: 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: \[ C_{final} = \frac{5}{9}(-56 - 32) = \frac{5}{9}(-88) = -48.89 \]

Step 5: 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°C.

Key Concepts

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 \( 27.22\)°C in just two minutes.
• In another case, Browning experienced a sudden drop by approximately \(-55.56\)°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.