Question

The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?

l. A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 5/9 degree Celsius.
ll. A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
lll. A temperature increase of 5/9 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.
A) I only
B) II only
C) III only
D) I and II only

Answer 1

D. I and II only

Explanation:

Give:- C= 5/9( f - 32 )

--> F = 9/5c + 32

(I) If F' = F + 1

C' = 5/9( F' - 32)

C' = 5/9( F - 32) + 5/9 x 1

C' = C + 5/9

The temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 5/9 degree Celsius

THEREFORE, STATEMENT | IS TRUE.

(II) If C'= C + 1

F' = 9/5C' + 32

F' = ( 9/5C + 32 ) + 9/5

F' = F + 9/5

F' = F + 1.8

The temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.

THEREFORE, STATMENT || IS TRUE

(III) If F' = F + 5/9

C' = 5/9 (F' - 32)

C' = 5/9 ( F - 32 ) + 5/9 x 5/9

C' = C + 25/81

The temperature increase of 5/9 degrees Fahrenheit is equivalent to a temperature increase of 25/81 degree Celsius.

THEREFORE, STATEMENT ||| IS FALSE