On a temperature scale ' X '. The boiling point of water is $65^{\circ} \mathrm{X}$ and the freezing point is $-15^{\circ} \mathrm{X}$. Assume that the X scale is linear. The equivalent temperature corresponding to $-95^{\circ} \mathrm{X}$ on the Farenheit scale would be:

(D) $-148^{\circ} \mathrm{F}$

(B) $-112^{\circ} \mathrm{F}$

JEE Main · 2023 · 11 Apr 2023 · Shift 1 · Heat & Thermodynamics

On a temperature scale ' X '. The boiling point of water is

6 5^{\circ} X

and the freezing point is

- 1 5^{\circ} X

. Assume that the X scale is linear. The equivalent temperature corresponding to

- 9 5^{\circ} X

on the Farenheit scale would be:

Answer: (D)

On a linear scale the same physical temperature keeps the same fractional position between the freezing and boiling points, so

\frac{X - X _{f r}}{X _{b p} - X _{f r}} = \frac{F - 32}{212 - 32}

. With

X_{f r} = - 1 5^{\circ}

X_{b p} = 6 5^{\circ}

X and

X = - 9 5^{\circ}

X, the left side is

\frac{- 95 - ( - 15 )}{65 - ( - 15 )} = \frac{- 80}{80} = - 1

. Then

F - 32 = 180 (- 1) = - 180

, giving

F = - 14 8^{\circ}

JEE Main · 2023 · 11 Apr 2023 · Shift 1 · Single correct option