Question

Temperature at which Fahrenheit and kelvin pair of scales give the same reading will be

• A. $\theta =-40$
• B. $\theta =40$
• C. $\theta =574.25$
• D. $\theta =512.45$

Answer 1

The correct option is C $\theta =574.25$

We know,

$\frac{c}{5}=\frac{F-32}{9}$

F-fahrenheit Temperature

C- Celsius Temperature

$\therefore$$F=\frac{9}{5}C+32=1.8C+32$

Also,

$C=T-273.15$

Where T= Kelvin temperature

$\therefore$$F=1.8(T-273.15)+32=1.8T-459.67$

Now, When F=T then,

$T=1.8T-459.67\therefore T=\frac{459.67}{0.8}=574.25\therefore 574.25°F=574.25K$