Question

The temperature at which Fahrenheit and Kelvin scales give the same reading is 570.
A. True
B. False

Answer 1

Hint:Use the formulae for converting the temperature in Celsius scale to Kelvin scale and to Fahrenheit scale to Kelvin scale. We have given that at a particular temperature, the Fahrenheit and Kelvin scales give the same readings. Equate the conversion formulae and determine that particular temperature in degree Celsius and then convert that temperature into Fahrenheit and Kelvin scales.

Formulae used:
The formula for converting the temperature in Celsius scale to Kelvin scale is
$$K=C+273.15$$ …… (1)
Here, $$K$$ is the temperature in Kelvin and $$C$$ is the temperature in Celsius.
The formula for converting the temperature in Fahrenheit scale to Kelvin scale is
$$F={\displaystyle \frac{9}{5}}C+32$$ …… (2)
Here, $$F$$ is the temperature in Fahrenheit and $$C$$ is the temperature in Celsius.

Complete step by step answer:
We have given that at a particular temperature, the Fahrenheit scale and Kelvin scale gives the same reading.
Equate the temperatures in Fahrenheit scale and Kelvin scale to determine that particular temperature.
$$K=F$$
Substitute $$C+273.15$$ for $$K$$ and $${\displaystyle \frac{9}{5}}C+32$$ for $$F$$ in the above equation.
$$C+273.15={\displaystyle \frac{9}{5}}C+32$$
$$\Rightarrow C-{\displaystyle \frac{9}{5}}C=32-273.15$$
$$\Rightarrow {\displaystyle \frac{5C-9C}{5}}=-241.15$$
$$\Rightarrow -4C=-241.15\times 5$$
$$\Rightarrow C={301.43}^{\circ }\text{C}$$
Hence. The temperature at which the Fahrenheit scale and Kelvin scale gives the same reading is $${301.43}^{\circ }\text{C}$$ in Celsius scale.
We can calculate the value of this temperature in Kelvin scale and Fahrenheit scale using equation (1) and (2).
Substitute $${301.43}^{\circ }\text{C}$$ for $$C$$ in equation (1).
$$K={301.43}^{\circ }\text{C}+273.15$$
$$\Rightarrow K={574.58}^{\circ }\text{K}$$
$$\Rightarrow K\approx {570}^{\circ }\text{K}$$
Substitute $${301.43}^{\circ }\text{C}$$ for $$C$$ in equation (2).
$$F={\displaystyle \frac{9}{5}}\left({301.43}^{\circ }\text{C}\right)+32$$
$$\Rightarrow F=542.57+32$$
$$\Rightarrow F={574.57}^{\circ }\text{F}$$
$$\therefore F\approx {570}^{\circ }\text{F}$$
Hence, the temperature at which the Fahrenheit scale and the Kelvin scale shows the same reading is $$570$$.

Hence, the option A is correct.

Note:The students should not forget to convert the temperature obtained in degree Celsius into the Fahrenheit and Kelvin scale. Otherwise, the final answer will not be correct. One can also use any two conversion formulae for converting the temperature in one scale to another scale and then determine the temperature at which the two Fahrenheit and Kelvin scales show the same reading.