What is the temperature of the triple point of water on an absolute scale whose unit interval size is equal to that of the Fahrenheit scale?

Solution

Let T_F be the temperature on Fahrenheit scale and T_K be the temperature on absolute scale.
Both the temperatures can be related as,
(T_F - 32) / 180 = (T_K - 273.15) / 100 ...(i)

Let T_F1 be the temperature on Fahrenheit scale and T_K1 be the temperature on absolute scale.
Both the temperatures can be related as,
(T_F1 - 32) / 180 = (T_K1 - 273.15) / 100 ...(ii)

Given that,
T_K1 – T_K = 1 K
Subtracting equation (i) from equation (ii), we get
(T_F1 - T_F) / 180 = (T_K1 - T_K) / 100 = 1 / 100
T_F1 - T_F = (1 ×180) / 100 = 9/5
Triple point of water = 273.16 K
∴ Triple point of water on absolute scale = 273.16 × (9/5) = 491.69

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