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  4. The temperature which has same numerical value on Celsius and Fahrenheit scale is

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Q. The temperature which has same numerical value on Celsius and Fahrenheit scale is

Thermal Properties of Matter

Solution:

Let $T$ be the same numerical value of temperature on Celsius scale and Fahrenheit scale. Then using the relation
$\frac{^{\circ}C}{100}=\frac{^{\circ}F-32}{180}$
According to question
$^{\circ}C=^{\circ}F=T$
$\therefore \frac{T}{100}=\frac{T-32}{180}$
$\therefore T=-40\,{}^{\circ}C=-40^{\circ}F$