Question

On a linear temperature scale $Y$, water freezes at $-160^{\circ}$ $Y$ and boils at $-50^{\circ}\, Y$. On this $Y$ scale, a temperature of $340\, K$ would be read as : (water freezes at $273\, K$ and boils at $373\, K$)

• A. $-73.7^{\circ}\, Y$
• B. $-233.7^{\circ}\, Y$
• C. $-86.3^{\circ}\, Y$
• D. $-106.3^{\circ}\, Y$

Answer 1

Answer: (C)

$\frac{Reading \,on \,any \,scale\, -\, LFP}{UFP-LFP}$
= constant for all scales
$\frac{340-273}{373-273} = \frac{^{\circ}y-\left(-160\right)}{-50-\left(-160\right)}$
$\Rightarrow \frac{67}{100} = \frac{y + 160 }{110}$
$\therefore \quad y=-86.3^{\circ}y$