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

Hint: Degree celsius, fahrenheit and kelvin are all units of temperature of which kelvin is the SI unit. The units are interchangeable. Kelvin and fahrenheit can be expressed in terms of degree celsius. Using the relationship between them we equate fahrenheit and kelvin in terms of degree Celsius to find the temperature which gives the same values for fahrenheit and kelvin.

Formulas used:
$\dfrac{9}{5}C+32=F$
$C+273=K$

Complete step-by-step solution:
The hotness or coldness of a body is measured by a physical property called temperature. Its SI unit is kelvin ($K$).
There are other scales in which temperature can be measured. They are degree celsius (${}^{o}C$) and fahrenheit ($F$).

Temperature is inter convertible between different units-
Converting degree celsius to fahrenheit as-
$\dfrac{9}{5}C+32=F$ - (1)
Here,
$C$ is temperature in degree Celsius
$F$ is temperature in Fahrenheit

Converting degree Celsius to kelvin as-
$C+273=K$ - (2)
Here,
$K$ is temperature in kelvin

The same reading on Fahrenheit and kelvin scale is given for-
From eq (1) and eq (2), we get,
$\begin{align}
  & F=K \\
 & \Rightarrow \dfrac{9}{5}C+32=C+273 \\
 & \Rightarrow \dfrac{9}{5}C-C=273-32 \\
 & \Rightarrow \dfrac{4}{5}C=241 \\
 & \therefore C={{301.25}^{o}}C \\
\end{align}$

Therefore, Fahrenheit and kelvin scales give the same reading at ${{301.25}^{o}}C$.

Additional information:
When the state of a body changes, the temperature remains constant. The heat is used to transform from one state to the other instead of raising the temperature. The heat required to change states is called latent heat, while the heat required to change temperature by a unit is called specific heat.

Note:
Temperature indicates the direction in which heat energy flows. The flow of heat energy takes place from a hotter body to a colder body. Temperature is an intensive quantity, i.e. it does not depend on the mass or quantity. The kelvin scale is also known as the absolute temperature scale because the absolute zero temperature of a body coincides with $0K$.