C=
5
9
(F−32)
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?
A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of
5
9
degree Celsius.
A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
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
Answers
Given:- C=
9
5
(F−32)
⇒F=
5
9
C+32
(I) If F' = F + 1
C
′
=
9
5
(F
′
−32)
C
′
=
9
5
(F+1−32)
C
′
=
9
5
(F−32)+
9
5
×1
C
′
=C+
9
5
Hence, a temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of
9
5
degree Celsius.
Therefore, statement I is true.
(II) If C' = C + 1
F
′
=
5
9
C
′
+32
F
′
=
5
9
(C+1)+32
F
′
=(
5
9
C+32)+
5
9
F
′
=F+
5
9
F
′
=F+1.8
Hence, a temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
Therefore, statement II is true.
(III) If F
′
=F+
9
5
C
′
=
9
5
(F
′
−32)
C
′
=
9
5
(F+
9
5
−32)
C
′
=
9
5
(F−32)+
9
5
×
9
5
C
′
=C+
81
25
Hence, a temperature increase of
9
5
degree Fahrenheit is equivalent to a temperature increase of
81
25
degree Celsius.
Therefore, statement III is false.