Question 680: Thermodynamics & KTG

Question

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

Accepted Answer

The temperature of a body on Kelvin scale = $x$ K
On Fahrenheit scale = $x$ $^{\circ} F$
Find $x$.
Step 1: Relation between Kelvin and Celsius
$ T(^{\circ}C) = T(K) - 273 $
So if $T = x$ K, then $T = x - 273$ $^{\circ}C$.
Step 2: Relation between Celsius and Fahrenheit
$ T(^{\circ}F) = \frac{9}{5} T(^{\circ}C) + 32 $
So,
$ x = \frac{9}{5}(x - 273) + 32 $
Step 3: Simplify
$ x = \frac{9}{5}x - \frac{9}{5} \cdot 273 + 32 $
$ x - \frac{9}{5}x = - \frac{9}{5}\cdot 273 + 32 $
$ \left(1 - \frac{9}{5}\right)x = -\frac{9}{5}\cdot 273 + 32 $
$ \left(-\frac{4}{5}\right)x = -\frac{2457}{5} + 32 $
$ \left(-\frac{4}{5}\right)x = -491.4 + 32 $
$ \left(-\frac{4}{5}\right)x = -459.4 $
Step 4: Solve for $x$
$ x = \frac{-459.4 \cdot 5}{-4} $
$ x = \frac{2297}{4} \approx 574.25 $
Final Answer:
$ x \approx 574 $
Ã¢ÂÂ Correct Option:
C (574)

Answer

40

Answer

313

Answer

574

Answer

301

Thermodynamics & KTG

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

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