Question

The temperature of a body on Kelvin scale is ' $x\text{ }K$ '. When it is measured by a Fahrenheit thermometer, it is found to be ' $x\text{ }^\circ\text{F}$ '. The value of ' $x$ ' is (nearly)}

• A. $40$
• B. $313$
• C. $574$
• D. $301$

Hint:

If the same numerical value appears on two temperature scales, set both scale-conversion formulas equal and solve.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Conversion between different temperature scales is linear. We set the value in Kelvin equal to the value in Fahrenheit.
Step 2: Key Formula or Approach:
$\frac{K - 273}{5} = \frac{F - 32}{9}$.
Step 3: Detailed Explanation:
Substitute $K = x$ and $F = x$:
\[ \frac{x - 273}{5} = \frac{x - 32}{9} \]
\[ 9x - 2457 = 5x - 160 \implies 4x = 2297 \implies x \approx 574.25 \]
Step 4: Final Answer:
The value is nearly 574.