Question

Two absolute scales A and B have triple points defined to be 200A and 300B. A temperature is measured on these scales as ${T_A}$ and ${T_B}$. What is the relation between ${T_A}$ and ${T_B}$? Given that triple point of water is = 276.16 K

Answer 1

Hint: Triple point is the point at which all three phases of water which are solid, liquid and gas coexist together. Two absolute scales are provided and the triple points of water on these absolute scales are given in reference to the triple point in Kelvin scale. We need to compare these absolute scales with the Kelvin scale and obtain an equation which compares the two absolute scales.

Complete step by step answer:
Temperature is the measurement of warmth or coolness of a system. There are several units of temperatures such as Kelvin, Celsius and Fahrenheit. Celsius and Fahrenheit are the common units of temperature which are used in day to day life, while Kelvin is its SI unit. The triple point of water is the particular point of temperature and pressure of water at which all of the phases of water that are solid, liquid and gaseous phase remain and coexist in equilibrium. The temperature value at the triple point of water is 276.16K. Here, on the two absolute scales, the triple point of water is defined as 200A and 300B respectively. Now,
\[
{T_1} = {T_k} \\
\Rightarrow 200A = 273.16
\]
Similarly, we have
\[
{T_2} = {T_k} \\
\Rightarrow 300B = 273.16
\]
Comparing the two above equations and forming the equation below, we get;
\[
 \dfrac{{273.16}}{{200}} \times {T_A} = \dfrac{{273.16}}{{300}} \times {T_B} \\
 \therefore {T_A}:{T_B} = 2:3 \\
 \]
Thus, the relationship between the two temperatures is of the ratio of the temperatures as 2:3.

Note: Such absolute scales are only used for dimensional analysis and comparisons with other scales but these scales do not have any industrial or day to day common uses as the three scales used are Kelvin, Celsius and Fahrenheit.