Suppose you are hiking down the Grand Canyon. At the top, the temperature early in the morning is a cool 3.36 °C. By late afternoon, the temperature at the bottom of the canyon has warmed to a sweltering 33.1 °C. What is the difference between the higher and lower temperatures in (a) Fahrenheit degrees and (b) kelvins?
To find the difference in Fahrenheit degrees, we need to convert the temperatures from Celsius to Fahrenheit:
(a) Fahrenheit:
1. Convert the higher temperature from Celsius to Fahrenheit:
°F = (°C × 9/5) + 32
°F = (33.1 × 9/5) + 32
°F = 91.78 °F (rounded to two decimal places)
2. Convert the lower temperature from Celsius to Fahrenheit:
°F = (°C × 9/5) + 32
°F = (3.36 × 9/5) + 32
°F = 37.41 °F (rounded to two decimal places)
3. Subtract the lower temperature from the higher temperature to find the difference in Fahrenheit degrees:
Difference = Higher temperature - Lower temperature
Difference = 91.78 °F - 37.41 °F
Difference = 54.37 °F (rounded to two decimal places)
Therefore, the difference between the higher and lower temperatures in Fahrenheit degrees is approximately 54.37 °F.
(b) Kelvin:
To find the difference in kelvins, we need to add 273.15 to each temperature, as Kelvin is the absolute temperature scale:
1. Convert the higher temperature from Celsius to Kelvin:
K = °C + 273.15
K = 33.1 + 273.15
K = 306.25 K (rounded to two decimal places)
2. Convert the lower temperature from Celsius to Kelvin:
K = °C + 273.15
K = 3.36 + 273.15
K = 276.51 K (rounded to two decimal places)
3. Subtract the lower temperature from the higher temperature to find the difference in kelvins:
Difference = Higher temperature - Lower temperature
Difference = 306.25 K - 276.51 K
Difference = 29.74 K (rounded to two decimal places)
Therefore, the difference between the higher and lower temperatures in kelvins is approximately 29.74 K.
To find the difference between the higher and lower temperatures in Fahrenheit degrees and kelvins, we need to convert the given temperatures from Celsius to the desired units and then calculate the difference.
(a) Fahrenheit degrees:
To convert Celsius to Fahrenheit, we can use the formula:
°F = (°C * 9/5) + 32
First, let's convert the higher temperature (33.1 °C) to Fahrenheit:
°F = (33.1 * 9/5) + 32 = 91.58 °F
Next, we'll convert the lower temperature (3.36 °C) to Fahrenheit:
°F = (3.36 * 9/5) + 32 = 38.61 °F
Now we can calculate the difference:
Difference in Fahrenheit = higher temperature (in °F) - lower temperature (in °F)
Difference in Fahrenheit = 91.58 °F - 38.61 °F = 52.97 °F
Therefore, the difference in Fahrenheit degrees is approximately 52.97 °F.
(b) Kelvins:
To convert Celsius to Kelvin, we can use the formula:
K = °C + 273.15
First, let's convert the higher temperature (33.1 °C) to Kelvin:
K = 33.1 + 273.15 = 306.25 K
Next, we'll convert the lower temperature (3.36 °C) to Kelvin:
K = 3.36 + 273.15 = 276.51 K
Now we can calculate the difference:
Difference in Kelvin = higher temperature (in K) - lower temperature (in K)
Difference in Kelvin = 306.25 K - 276.51 K = 29.74 K
Therefore, the difference in kelvins is approximately 29.74 K.