Question

A new scale of temperature called time is introduced. The reading on new scale is twice the reading on celsius scale when the temperature of a certain body is 373K. The reading on fahrenheit scale is 17/15th the reading on time scale when the temperature of body is 20oC Determine upper fixed point and lower fixed point of time scale.please answer soon tomorrow exam

Answer 1

The new scale is called time.

The reading on new scale is twice the reading on celsius scale when the temperature of a certain body is 373K.
When temperature is 373K(boiling point of water), reading on celsius scale = 100
so reading on time scale = 100×2 = 200

The reading on fahrenheit scale is 17/15th the reading on time scale when the temperature of body is 20⁰C.
reading on fahrenheit scale for 20⁰C = (9×20)/5 + 32 = 36+32 = 68
reading on time scale =68×(15/17) = 60

Upper fixed point of a scale is boiling point of water. In time scale, it is 200.
Lower fixed point of a scale is freezing point of water. Let it be L.
we found that, 20⁰C = 60 on time scale. thus

$\frac{60-L}{200-L} = \frac{20-0}{100-0}\\ \\ \frac{60-L}{200-L} = \frac{1}{5} \\ \\ 5 \times (60-L)=200-L \\ \\300-5L=200-L\\ \\300-200=5L-L\\ \\4L=100\\ \\L= \frac{100}{4}=25$

So lower fixed point in time scale is 25.