Question

Q15. a) Find the temperatures for which the readings in Celsius and Fahrenheit scales differ by 5°
​

Answer 1

Answer:

To find:

The temperatures for which the readings in Celsius and Fahrenheit scales differ by 5°

Calculation:

Case 1 : (When C - F = 5°)

$\therefore \: \rm{ \dfrac{C}{5} = \dfrac{F - 32}{9} }$

$= > \: \rm{ \dfrac{5 + F}{5} = \dfrac{F - 32}{9} }$

$\rm{ = > 45 + 9F = 5F - 160}$

$\rm{ = > 9F - 5F = - 160 - 45}$

$\rm{ = > 4F = - 205}$

$\boxed{ \rm{ = > F = - {51.25}^{ \circ} }}$

So, C = (5 + F) = (5 - 51.25) = 46.25°

Case 2:( F - C = 5°)

$\therefore \: \rm{ \dfrac{C}{5} = \dfrac{F - 32}{9} }$

$= > \: \rm{ \dfrac{C}{5} = \dfrac{(5 + C) - 32}{9} }$

$= > \: \rm{ \dfrac{C}{5} = \dfrac{C- 27}{9} }$

$= > \: \rm{ 9C= 5C - 135 }$

$= > \: \rm{ 4C = - 135 }$

$\boxed{ = > \: \rm{ C = - {33.75}^{ \circ} }}$

F = (5 + C) = -28.75°