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Q. The temperature at which Celsius reading is half theifahrenheit reading

Thermal Properties of Matter

Solution:

Let at temperature $x ^{\circ} C$, Celsius scale is half of that on Fahrenheit scale, We have relation between Celsius scale and Fahrenheit scale,
$
\frac{ T _{ C }-0}{100}=\frac{ T _{ F }-32}{180}
$
As Celsius scale is half of that on Fahrenheit scale i.e. Fahrenheit scale is double of that on Celsius scale,
Hence, $T _{ F }=2 x ^{\circ} F$,
$
\frac{x-0}{100}=\frac{2 x-32}{180}
$
or $x =160^{\circ} C$,