At what temperature is the Fahrenheit scale reading equal to the reading on the Celsius scale?

Text Solution

Answer : A::B::C::D

Solution : (a) `(T_C - 0)/(100) = (T_F -32)/(180)` <br> Putting `T_F = (T_C)/2`, we get `T_C = 160^@ C` <br> (b) Putting `T_F = (T_C)/2`, we get `T_C = -24.6^@ C`.

Answer

Verified

Hint: To find the solution to this problem at first, we should know the relation between the Fahrenheit and Celsius. Then assume that the Fahrenheit scale is equal to half of the Celsius scale, after this with some basic calculation we can find the temperature at which the Fahrenheit scale reading is equal to half of the Celsius scale.

Formula used: \[{{T}_{c}}=\left( T-32 \right)\text{x}\dfrac{5}{9}\]

where\[{{T}_{c}}\]= the Celsius temperature \[T\] = Fahrenheit temperature

Complete step by step answer:

To get the temperature at which the Fahrenheit scale will read half of Celsius scale, let us assume, \[T=\dfrac{{{T}_{c}}}{2}......(1)\] Now, from the relation between the Fahrenheit and Celsius scale we know that, \[{{T}_{c}}=(T-32)\text{x}\dfrac{5}{9}......(2)\]Now, putting the value of equation (1) in (2) we get,\[\begin{align} & {{T}_{c}}=\left( \dfrac{{{T}_{c}}}{2}-32 \right)\text{x}\dfrac{5}{9} \\ & \Rightarrow 9{{T}_{c}}=\dfrac{5({{T}_{c}}-64)}{2} \\ & \Rightarrow 9{{T}_{c}}=\dfrac{5}{2}{{T}_{c}}-160 \\ & \Rightarrow {{T}_{c}}=-24.6\text{C} \\ \end{align}\]Therefore, the temperature at which the Fahrenheit scale reading is equal to half of the Celsius scale is $-{{24.6}^{\circ }}C$ .

Additional Information:

The Fahrenheit scale is defined by two fixed points:-(a) the temperature at which pure water freezes into ice is defined as ${{32}^{\circ }}F$, and(b) the boiling point of water is defined as${{212}^{\circ }}F$, both at sea level and under standard atmospheric pressure. Celsius scale is a temperature scale that has a freezing point of water at ${{0}^{\circ }}C$ and the boiling point of water at ${{100}^{\circ }}C$.

Note:

The temperature at which the Fahrenheit scale is equal to the Celsius scale is $-{{24.6}^{\circ }}C$. One of the key points to remember here is the conversion formula between the Fahrenheit scale and the Celsius scale. After this most of the work is done through simple arithmetic