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Q17 (CISF/2019) Science & Technology › Basic Science (Physics, Chemistry, Biology)

A Kelvin thermometer and a Fahrenheit thermometer both give the same reading for a certain sample. The corresponding Celsius temperature is about

Explanation

To find the temperature where the Kelvin (K) and Fahrenheit (F) scales provide the same reading, we use their relationship with the Celsius (C) scale:

  • K = C + 273.15
  • F = (9⁄5 × C) + 32

Let the common reading be x, such that K = F = x. From the first equation, C = x - 273.15. Substituting this into the second equation:

x = 9⁄5(x - 273.15) + 32

Solving for x:
5x = 9(x - 273.15) + 160
5x = 9x - 2458.35 + 160
4x = 2298.35
x ≈ 574.59

The corresponding Celsius temperature (C) is:
C = x - 273.15 = 574.59 - 273.15 = 301.44 °C.

Thus, the temperature is approximately 301 °C. Options B, C, and D are mathematically incorrect based on the standard conversion formulas.

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SIMILAR QUESTIONS

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