Question

Figure shows three temperature scales with the freezing and boiling point of water indicated. A change of ${25}^{\circ }P,{25}^{\circ }Q,{25}^{\circ }R$ are denoted by $X_1,X_2,X_3$ respectively. Which of the following is correct?

• A. $X_1<X_2<X_3$
• B. $X_1>X_2>X_3$
• C. $X_1=X_2=X_3$
• D. $X_1>X_2=X_3$

Answer 1

The correct option is B $X_1>X_2>X_3$


We know,
$UFP-LFP={100}^{\circ }K$ for water on any temperature scale.
$\therefore {20}^{\circ }P-(-{80}^{\circ }P)={100}^{\circ }K$
$\Rightarrow 1^{\circ }P=1^{\circ }K$
$\therefore {25}^{\circ }P={25}^{\circ }K=X_1$

Simillarly,
${120}^{\circ }Q-\left({50}^{\circ }Q\right)={100}^{\circ }K$
$\Rightarrow 1^{\circ }Q={\frac{100}{70}}^{\circ }K$
$\therefore {25}^{\circ }Q=25\times {\frac{100}{70}}^{\circ }K=X_2$

and,
${300}^{\circ }R-\left({225}^{\circ }R\right)={100}^{\circ }K$
$\Rightarrow 1^{\circ }R={\frac{100}{75}}^{\circ }K$
$\therefore {25}^{\circ }R=25\times {\frac{100}{75}}^{\circ }K=X_3$

$\therefore X_1>X_2>X_3$