(b) Calculate the one temperature at which Fahrenheit and Kelvin thermometers agree with each other

Verified step by step guidance

1. Convert the Fahrenheit temperature to Kelvin using the conversion formula: \( K = \frac{5}{9} \times (F - 32) + 273.15 \).
2. Set up an equation where the Fahrenheit temperature (F) is equal to the Kelvin temperature (K) derived from the conversion formula: \( F = \frac{5}{9} \times (F - 32) + 273.15 \).
3. Simplify the equation to isolate F. Start by multiplying both sides by 9 to clear the fraction.
4. Next, move all terms involving F to one side of the equation to facilitate solving for F.
5. Solve the resulting equation for F to find the temperature at which Fahrenheit and Kelvin scales agree.

Key Concepts

Temperature Scales

Temperature can be measured using different scales, the most common being Celsius, Fahrenheit, and Kelvin. Each scale has its own zero point and increments, which can lead to confusion when converting between them. Understanding how these scales relate to one another is crucial for solving problems involving temperature.

Conversion Formulas

To find the temperature at which Fahrenheit and Kelvin agree, one must use the conversion formulas between these scales. The formula for converting Fahrenheit (F) to Celsius (C) is F = (C × 9/5) + 32, and for Celsius to Kelvin (K), it is K = C + 273.15. These formulas allow for the necessary calculations to determine the point of agreement.

Point of Agreement

The point at which two temperature scales agree is a specific temperature where their numerical values are the same. In this case, it involves finding a temperature that satisfies both the Fahrenheit and Kelvin scales simultaneously. This concept is essential for understanding how different temperature measurements can align under certain conditions.