On a linear temperature scale $\mathrm{Y}$, water freezes at $-160^{\circ} \mathrm{Y}$ and boils at…
On a linear temperature scale $\mathrm{Y}$, water freezes at $-160^{\circ} \mathrm{Y}$ and boils at $-50^{\circ} \mathrm{Y}$. On this $\mathrm{Y}$ scale, a temperature of $340 \mathrm{~K}$ would be read as : (water freezes at $273 \mathrm{~K}$ and boils at $373 \mathrm{~K}$ )
$-73.7^{\circ} \mathrm{Y}$
$-233.7^{\circ} \mathrm{Y}$
$-86.3^{\circ} \mathrm{Y}$
$-106.3^{\circ} \mathrm{Y}$
Solution
Reading on any scale - LFP
UFP - LFP
$=$ constant for all scales
$\frac{340-273}{373-273}=\frac{{ }^{\circ} \mathrm{y}-(-160)}{-50-(-160)}$
$\Rightarrow \frac{67}{100}=\frac{\mathrm{y}+160}{110}$
$\therefore \quad y=-86.3^{\circ} \mathrm{y}$