Thermodynamics 5

$\large \text {Suppose Fahrenheit and kelvin will give the same value at the temperature of}$ $\huge\color{#D61F06}P.$

$\large\text{So,}F=K=P$

$\large\text{we know that,}$

$\large \dfrac{F-32}{9} = \dfrac{K-273}{5}$

$\large \Rightarrow \dfrac{P-32}{9}$ = $\dfrac{P-273}{5}$

$\large \Rightarrow 9P-2457 =5P-160$

$\large \Rightarrow 4P=2297$

$\large \Rightarrow P=574.25$

$\large\text{So}, \boxed{F= 574.25^\circ F} ~ \text{and also} ~ \boxed{K= {574.25}^\circ K}$

$\large \text{with the mathematical calculation now we can say that} \boxed{\text{B and C scale will have the same value.}}$

We know that the given temperatures are the melting and boiling points for water at standard pressure in Celsius, Fahrenheit, and Kelvin respectively.