Temperature Increase Conversion: Fahrenheit to Kelvin

This solution explains how to convert a temperature increase given in degrees Fahrenheit ($^\circ F$) to Kelvin (K). We are given a temperature increase of $45 \text{ }^\circ F$ during a chemical reaction and need to find the equivalent increase in Kelvin.

Understanding Temperature Scale Changes

It's important to remember the difference between converting an absolute temperature and a temperature *change* (or increase/decrease).

• The formula to convert a temperature from Fahrenheit ($F$) to Celsius ($C$) is: $C = \frac{5}{9}(F - 32)$
• The formula to convert a temperature from Celsius ($C$) to Kelvin ($K$) is: $K = C + 273.15$
• However, when dealing with a *change* or *increase* in temperature, the conversion is simpler. A change in temperature in Fahrenheit ($\Delta F$) relates directly to a change in Celsius ($\Delta C$) as follows: $\Delta C = \frac{5}{9} \Delta F$
• Crucially, the size of one degree Celsius is exactly the same as the size of one Kelvin. This means a *change* in temperature in Celsius is equal to the *change* in temperature in Kelvin: $\Delta K = \Delta C$

Step-by-Step Calculation for Temperature Increase

Let's calculate the temperature increase step-by-step:

1. Identify the given temperature increase: The problem states the temperature increase is $45 \text{ }^\circ F$. So, $\Delta F = 45 \text{ }^\circ F$.
2. Convert the Fahrenheit increase to Celsius: Using the formula $\Delta C = \frac{5}{9} \Delta F$, we substitute the given value: $ \Delta C = \frac{5}{9} \times 45 \text{ }^\circ F $ Performing the multiplication: $ \Delta C = 5 \times 5 \text{ }^\circ C $ $ \Delta C = 25 \text{ }^\circ C $ So, the temperature increase is $25 \text{ }^\circ C$.
3. Convert the Celsius increase to Kelvin: As established earlier, the change in temperature in Kelvin ($\Delta K$) is equal to the change in temperature in Celsius ($\Delta C$). $ \Delta K = \Delta C $ Therefore, the temperature increase in Kelvin is: $ \Delta K = 25 \text{ K} $

Final Result

The temperature increase of $45 \text{ }^\circ F$ is equivalent to a temperature increase of $25 \text{ K}$.