Question

Figure shows three temperature scales with the freezing and boiling point of water indicated. A change of 25 R⁰, 25 S⁰ and 25 U⁰ is denoted by $x_1$, $x_2$, $x_3$ respectively. Which of the following is correct:

• A. $x_1 > x_2 > x_3$
• B. $x_2 < x_1 < x_3$
• C. $x_3 > x_2 > x_1$
• D. can not be predicted

Answer 1

Answer: (C)

$x_3 > x_2 > x_1$

Answer 2

The freezing and boiling points of water are 0°C and 100°C, respectively, giving a range of 100°C.

For scale R: Freezing point = -80°R, Boiling point = 120°R. Range = $120 - (-80) = 200$ R⁰. Conversion: 200 R⁰ = 100°C $\implies$ 1 R⁰ = 0.5°C. $x_1 = 25$ R⁰ $= 25 \times 0.5$ °C $= 12.5$ °C.

For scale S: Freezing point = 50°S, Boiling point = 225°S. Range = $225 - 50 = 175$ S⁰. Conversion: 175 S⁰ = 100°C $\implies$ 1 S⁰ = $\frac{100}{175}$ °C $= \frac{4}{7}$ °C. $x_2 = 25$ S⁰ $= 25 \times \frac{4}{7}$ °C $= \frac{100}{7}$ °C $\approx 14.286$ °C.

For scale U: Freezing point = 30°U, Boiling point = 120°U. Range = $120 - 30 = 90$ U⁰. Conversion: 90 U⁰ = 100°C $\implies$ 1 U⁰ = $\frac{100}{90}$ °C $= \frac{10}{9}$ °C. $x_3 = 25$ U⁰ $= 25 \times \frac{10}{9}$ °C $= \frac{250}{9}$ °C $\approx 27.778$ °C.

Comparing the values: $x_1 = 12.5$ °C $x_2 \approx 14.286$ °C $x_3 \approx 27.778$ °C

Therefore, $x_1 < x_2 < x_3$, which can also be written as $x_3 > x_2 > x_1$.