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AP EAMCET · PHYSICS · Thermal Properties of Matter

If the values of the temperature of a body in Fahrenheit and Celcius scales are in the ratio of \(13: 5\), then the temperature of the body is

  1. A \(80^{\circ} \mathrm{F}\)
  2. B \(104^{\circ} \mathrm{C}\)
  3. C \(40^{\circ} \mathrm{C}\)
  4. D \(40^{\circ} \mathrm{F}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(40^{\circ} \mathrm{C}\)

Step-by-step Solution

Detailed explanation

\( \frac{F}{C} = \frac{13}{5} \Rightarrow F = \frac{13}{5} C \) \( \frac{C}{5} = \frac{F-32}{9} \) \( \frac{C}{5} = \frac{\frac{13}{5}C-32}{9} \) \( 9C = 5(\frac{13}{5}C-32) \) \( 9C = 13C - 160 \) \( 4C = 160 \) \( C = 40^{\circ} \mathrm{C} \)
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