Question

How do you convert $ {{20}^{\circ }}C $ to the Fahrenheit scale ? \[\]

Answer 1

Hint: We recall the two temperature scales Celsius scale and Fahrenheit scale. We recall that we can convert from Celsius to Fahrenheit $ f=\dfrac{9}{5}\times c+32 $ . We take $ c={{20}^{\circ }}C $ and find the value in Fahrenheit scale using the formula .\[\]

Complete step by step answer:
We know that Celsius scale is a scale to measure temperature in unit called Celsius $ \left( ^{\circ }C \right) $ where boiling point of water corresponds to $ {{100}^{\circ }}C $ and freezing point of water corresponds to $ {{32}^{\circ }}C $ .Similarly Fahrenheit scale is a scale to measure temperature in unit called Fahrenheit $ \left( ^{\circ }F \right) $ where boiling point of water corresponds to $ {{32}^{\circ }}F $ and freezing point of water corresponds to $ {{212}^{\circ }}F $ . \[\]

The temperature difference between freezing point and boiling point in Celsius scale is
\[{{100}^{\circ }}C-{{0}^{\circ }}C=100\]
The temperature difference between freezing point and boiling point in Fahrenheit scale is $ {{212}^{\circ }}F-{{32}^{\circ }}F=180 $ \[\]
We know that the raised temperature of water from freezing point to boiling point is same and independent of scale. So we have $ {{100}^{\circ }}C={{180}^{\circ }}f\Rightarrow {{1}^{\circ }}C={{\left( \dfrac{180}{100} \right)}^{\circ }}F={{\left( \dfrac{9}{5} \right)}^{\circ }}F $ .Since initial point is $ {{0}^{\circ }}C={{32}^{\circ }}F $ we add $ {{32}^{\circ }} $ . So the conversion formula for from Celsius to Fahrenheit with $ {{c}^{\circ }}C $ as the measurement in Celsius scale as
\[{{f}^{\circ }}F=\dfrac{9}{5}\times {{c}^{\circ }}C+32\]
We are given in the question the measure of temperature in Celsius scale as $ {{20}^{\circ }}C $ . So the temperature in Fahrenheit scale will be
\[{{f}^{\circ }}=\dfrac{9}{5}\times 20+32=9\times 4+32=36+32={{68}^{\circ }}F\]
So $ {{20}^{\circ }}C $ is $ {{68}^{\circ }}F $ in the Fahrenheit scale. \[\]

Note:
 We note that we convert back from Fahrenheit to Celsius using the conversion formula $ c=\left( f-32 \right)\times \dfrac{5}{9} $ . We note the finding the value of $ {{1}^{\circ }}C $ in Fahrenheit scale by dividing follows unitary method with direct variation where value of single unit is obtained first by dividing. We note that Kelvin scale is SI unit of temperature where $ {{0}^{\circ }}K=-{{273}^{\circ }}C $ and $ {{100}^{\circ }}C={{373}^{\circ }}K $ .