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

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Understand the relationship between Fahrenheit and Kelvin scales. The Fahrenheit scale is related to the Celsius scale by the formula: \( F = \frac{9}{5}C + 32 \). The Kelvin scale is related to the Celsius scale by the formula: \( K = C + 273.15 \).

Set up the equation where Fahrenheit and Kelvin temperatures are equal: \( F = K \). Substitute the expressions for \( F \) and \( K \) in terms of \( C \) into this equation.

Substitute \( F = \frac{9}{5}C + 32 \) and \( K = C + 273.15 \) into the equation \( F = K \), resulting in \( \frac{9}{5}C + 32 = C + 273.15 \).

Solve the equation \( \frac{9}{5}C + 32 = C + 273.15 \) for \( C \). This involves isolating \( C \) on one side of the equation.

Once \( C \) is found, substitute it back into either the Fahrenheit or Kelvin formula to find the temperature at which both scales agree.

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주요 개념

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Temperature Scales

Temperature scales are systems for measuring temperature, with Fahrenheit and Kelvin being two common examples. Fahrenheit is used primarily in the United States, while Kelvin is the SI unit for temperature, used in scientific contexts. Understanding the conversion between these scales is crucial for solving problems involving temperature comparisons.

Conversion Formulas

Conversion formulas allow for the translation of temperature values between different scales. The formula to convert Fahrenheit to Kelvin is K = (F - 32) × 5/9 + 273.15. This formula is essential for determining the temperature at which Fahrenheit and Kelvin values are equal, requiring algebraic manipulation to find the common temperature.

Algebraic Manipulation

Algebraic manipulation involves rearranging equations to solve for unknown variables. In this context, it is used to equate the Fahrenheit and Kelvin conversion formulas and solve for the temperature at which they are equal. This process requires understanding how to isolate variables and perform operations to find the solution.