Question

On which temperature scale \(\left(^{\circ} \mathrm{F},^{\circ} \mathrm{C}, \text { or } \mathrm{K}\right)\) does 1 degree represent the smallest change in temperature?

Short answer

On the Fahrenheit scale \(\left(^{\circ} \mathrm{F}\right)\), 1 degree represents the smallest change in temperature, as it corresponds to a change of approximately 0.56 degrees Celsius (or Kelvin).

Step-by-step solution

Understanding Temperature Conversion Formulas

In order to compare the different temperature scales, we need to know the conversion formulas between them. The formulas for temperature conversion are as follows: 1. Celsius to Fahrenheit: \(F = \frac{9}{5}C + 32\) 2. Fahrenheit to Celsius: \(C = \frac{5}{9}(F - 32)\) 3. Celsius to Kelvin: \(K = C + 273.15\) 4. Kelvin to Celsius: \(C = K - 273.15\)

Analyze Change in Fahrenheit

Let's first consider a change of 1 degree in Fahrenheit, i.e., from \(F\) to \(F + 1\). We will convert this change to Celsius using the Fahrenheit to Celsius formula. Let the corresponding Celsius temperatures be \(C_1\) and \(C_2\): \(C_1 = \frac{5}{9}(F - 32)\) \(C_2 = \frac{5}{9}((F + 1) - 32)\) Now, we will find the difference in the Celsius temperatures, i.e., \(C_2 - C_1\): \(C_2 - C_1 = \frac{5}{9}(F + 1 - 32) - \frac{5}{9}(F - 32) = \frac{5}{9}\) So, a change of 1 degree Fahrenheit corresponds to a change of \(\frac{5}{9} \approx 0.56\) degrees Celsius.

Analyze Change in Celsius

Since Celsius and Kelvin scales have the same intervals between degrees, a change of 1 degree in Celsius will always correspond to a change of 1 degree in Kelvin. Therefore, a change of 1 degree Celsius corresponds to a change of 1 degree Kelvin.

Comparing Changes

We have found that: 1. A change of 1 degree Fahrenheit corresponds to a change of 0.56 degrees Celsius (or Kelvin) 2. A change of 1 degree Celsius corresponds to a change of 1 degree Kelvin As the change per degree increment is smallest in the Fahrenheit scale, we can conclude that on the Fahrenheit scale \(\left(^{\circ} \mathrm{F}\right)\), 1 degree represents the smallest change in temperature.

Key concepts

Celsius to Fahrenheit Conversion

Converting Celsius to Fahrenheit might seem tricky, but it's a simple process once you remember the formula: F = \( \frac{9}{5}C + 32 \). This formula is fundamental in understanding how temperature scales relate to each other. Let's say you have a temperature in Celsius, and you want to find out what that would be in Fahrenheit. Begin by multiplying the Celsius temperature by 9/5 (or 1.8). After you've done that, add 32 to the result, and voilà, you have the temperature in Fahrenheit.

For instance, to convert 20 degrees Celsius to Fahrenheit, first multiply 20 by 9/5 to get 36, then add 32 to reach a final answer of 68 degrees Fahrenheit. This can be especially handy in everyday life, like when you're following a recipe that uses Fahrenheit while your oven is marked in Celsius.

Fahrenheit to Celsius Conversion

To convert Fahrenheit to Celsius, you work with the formula: C = \( \frac{5}{9}(F - 32) \). This formula helps to transform a Fahrenheit temperature reading into Celsius. The process involves two steps. First, subtract 32 from the Fahrenheit temperature. Then, multiply the result by 5/9 (which is equal to the fraction 1/1.8).

For example, if you want to convert 95 degrees Fahrenheit to Celsius, you would first subtract 32 from 95, giving you 63. Then you multiply 63 by 5/9, resulting in 35 degrees Celsius. This conversion is often used in science classes and by international travelers who need to convert weather forecasts or cooking temperatures.

Understanding the Kelvin Temperature Scale

The Kelvin temperature scale is an absolute scale where 0 K is absolute zero, the theoretical point where particle motion stops. Unlike Celsius and Fahrenheit, it isn't referred to in degrees because it is an absolute scale. It uses the same increment size as Celsius, so converting between Celsius and Kelvin is straightforward: add 273.15 to your Celsius temperature to get Kelvin, or subtract 273.15 from your Kelvin temperature to get Celsius.

To convert 25 degrees Celsius to Kelvin, simply add 273.15, resulting in 298.15 K. The Kelvin scale is incredibly important in scientific contexts, as it provides an absolute measurement of temperature that's necessary for calculations in thermodynamics and related fields. Remember, since the size of a Kelvin is the same as a degree Celsius, a change by 1 Celsius is also a change by 1 Kelvin.