Chapter 2: Problem 34
The temperature outside is \(263.5 \mathrm{~K}\). What is the temperature in degrees Celsius and in degrees Fahrenheit?
Short Answer
Expert verified
The temperature outside is approximately -9.65 \(^\circ\)C in degrees Celsius and 14.63 \(^\circ\)F in degrees Fahrenheit.
Step by step solution
01
Convert Kelvin to degrees Celsius
To convert the temperature from Kelvin to degrees Celsius, we use the formula:
Celsius = Kelvin - 273.15
Plug in the given temperature in Kelvin:
Celsius = \(263.5 \mathrm{~K}\) - 273.15
Celsius ≈ -9.65
So, the temperature outside in degrees Celsius is approximately -9.65 \(^\circ\)C.
02
Convert degrees Celsius to degrees Fahrenheit
Now, we'll convert the temperature in degrees Celsius to degrees Fahrenheit using the formula:
Fahrenheit = (Celsius × 9/5) + 32
Plug in the temperature in degrees Celsius that we found in Step 1:
Fahrenheit = (-9.65 × 9/5) + 32
Fahrenheit ≈ 14.63
So, the temperature outside in degrees Fahrenheit is approximately 14.63 \(^\circ\)F.
03
Final answers
The temperature outside in degrees Celsius is approximately -9.65 \(^\circ\)C, and in degrees Fahrenheit, it's approximately 14.63 \(^\circ\)F.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Kelvin to Celsius Conversion
Understanding the relationship between Kelvin and Celsius is crucial for scientific studies and everyday weather reporting. Kelvin is a temperature scale often used in physics and represents the absolute thermodynamic scale. To convert a temperature from Kelvin to Celsius, one should subtract 273.15 from the Kelvin value. This number represents the absolute zero on the Celsius scale, which is equivalent to -273.15°C.
This is essential because it provides a straightforward way to translate theoretical, absolute temperatures into more commonly used Celsius temperatures. For example, a temperature of zero Kelvin represents the point where theoretically particles would stop moving due to lack of thermal energy. This is a theoretical limit, not achievable in practice. When one wants to make sense of temperatures such as the outer space or the boiling point of a substance at standard atmospheric conditions, Kelvin to Celsius conversion becomes critical.
Considering the temperature exercise given, where the temperature outside is 263.5 K, it's essential to grasp that Kelvin to Celsius is not just a 'number trick'; it’s a transformation to a scale based on water's freezing and boiling points at standard pressure. This eases comprehension and explanation of temperature differences in a manner that's more tangible for everyday scenarios. Hence, the conversion formula is applied as follows: Celsius = Kelvin - 273.15 resulting in approximately -9.65°C.
This is essential because it provides a straightforward way to translate theoretical, absolute temperatures into more commonly used Celsius temperatures. For example, a temperature of zero Kelvin represents the point where theoretically particles would stop moving due to lack of thermal energy. This is a theoretical limit, not achievable in practice. When one wants to make sense of temperatures such as the outer space or the boiling point of a substance at standard atmospheric conditions, Kelvin to Celsius conversion becomes critical.
Considering the temperature exercise given, where the temperature outside is 263.5 K, it's essential to grasp that Kelvin to Celsius is not just a 'number trick'; it’s a transformation to a scale based on water's freezing and boiling points at standard pressure. This eases comprehension and explanation of temperature differences in a manner that's more tangible for everyday scenarios. Hence, the conversion formula is applied as follows: Celsius = Kelvin - 273.15 resulting in approximately -9.65°C.
Celsius to Fahrenheit Conversion
When converting temperatures from Celsius to Fahrenheit, we use a specific formula that adjusts for the different starting points and scaling of the two scales. The formula is: Fahrenheit = (Celsius × 9/5) + 32. The '+ 32' portion accounts for the offset between the freezing point of water on both scales — 0°C for Celsius and 32°F for Fahrenheit — while the '× 9/5' is the ratio of how many Fahrenheit degrees there are per Celsius degree.
For instance, in the given exercise, to convert -9.65°C (the previously converted temperature from Kelvin to Celsius) to Fahrenheit, it gets multiplied by 9/5 or 1.8 and then add 32, which results in approximately 14.63°F. This practice is especially common in countries still using the Fahrenheit scale, predominantly in the United States, where daily weather forecasts and cooking temperatures are given in Fahrenheit.
Understanding how to make these conversions is not only practical but also reinforces the relationship between different scales used across various regions. Knowing this could also be quite handy for travelers, enabling smooth transitions in understanding weather forecasts or cooking recipes from different parts of the world.
For instance, in the given exercise, to convert -9.65°C (the previously converted temperature from Kelvin to Celsius) to Fahrenheit, it gets multiplied by 9/5 or 1.8 and then add 32, which results in approximately 14.63°F. This practice is especially common in countries still using the Fahrenheit scale, predominantly in the United States, where daily weather forecasts and cooking temperatures are given in Fahrenheit.
Understanding how to make these conversions is not only practical but also reinforces the relationship between different scales used across various regions. Knowing this could also be quite handy for travelers, enabling smooth transitions in understanding weather forecasts or cooking recipes from different parts of the world.
Understanding Temperature Units
Temperature is a measure of how hot or cold an object is, and it's a critical factor in scientific studies as well as everyday life. Temperature units, such as Kelvin (K), Celsius (°C), and Fahrenheit (°F), are the scales by which temperature is measured. Each unit is part of a temperature scale that defines the start and endpoints based on specific physical phenomena.
The Kelvin scale is an absolute thermodynamic scale used widely in the scientific community because it starts at absolute zero, the temperature at which molecular motion stops. The Celsius scale, adopted in most countries worldwide, defines 0°C as the freezing point and 100°C as the boiling point of water at sea level. On the other hand, the Fahrenheit scale sets the freezing point of water at 32°F and the boiling point at 212°F, with a conversion formula to shift between different scales.
Each temperature unit serves its own purpose in different fields and regions. Scientists often use Kelvin for its definition based on natural phenomena, while everyday temperature contexts, like weather and cooking, commonly utilize Celsius or Fahrenheit. Understanding how to convert between these scales is not only a fundamental scientific skill but also part of being well-informed in a global context where different systems coexist.
The Kelvin scale is an absolute thermodynamic scale used widely in the scientific community because it starts at absolute zero, the temperature at which molecular motion stops. The Celsius scale, adopted in most countries worldwide, defines 0°C as the freezing point and 100°C as the boiling point of water at sea level. On the other hand, the Fahrenheit scale sets the freezing point of water at 32°F and the boiling point at 212°F, with a conversion formula to shift between different scales.
Each temperature unit serves its own purpose in different fields and regions. Scientists often use Kelvin for its definition based on natural phenomena, while everyday temperature contexts, like weather and cooking, commonly utilize Celsius or Fahrenheit. Understanding how to convert between these scales is not only a fundamental scientific skill but also part of being well-informed in a global context where different systems coexist.
