Question

find the temperature at which farenheit and Kelvin scales gives the same reading?​

Answer 1

To Find:

The temperature at which Fahrenheit and Kelvin scales gives the same reading

Solution:

Let x be the temperature at which Fahrenheit and Kelvin scales gives the same reading

Now, we know that

• Relation between Fahrenheit and Kelvin temperature scales is given by

$\longrightarrow\bf{\dfrac{F-32}{180}=\dfrac{K-273}{100}}$

where,

⫸ F is the temperature in Fahrenheit

⫸ K is the temperature in Kelvin

So, on using above expression, we get

$\longrightarrow\mathrm{\dfrac{x-32}{\cancel{180}}=\dfrac{x-273}{\cancel{100}}}$

$\longrightarrow\mathrm{\dfrac{x-32}{9}=\dfrac{x-273}{5}}$

$\longrightarrow\mathrm{5(x-32)=9(x-273)}$

$\longrightarrow\mathrm{5x-160=9x-2457}$

$\longrightarrow\mathrm{2457-160=9x-5x}$

$\longrightarrow\mathrm{2297=4x}$

$\longrightarrow\mathrm{4x=2297}$

$\longrightarrow\mathrm{x=\dfrac{2297}{4}}$

$\longrightarrow\mathrm{\pink{x=574.25}}$

Hence, the required temperature is 574.25°F or 574.25 K.