Similarly,

(20.8)

or,

(20.9)

or,

(20.10)

Then,

(20.11)

or,

(20.12)

In the above equation, does not appear on the left hand side. Therefore, on the right hand side, the dependence on should cancel out. Hence, the nature of function F is such that,

(20.13)

Then,

(20.14)

Therefore,

or,

(20.15)

So,

(20.16)

There is no further restriction on the function. The choice of the function now defines the temperature scale of interest.

If we choose

(20.17)

(20.18)

or,

(20.19)

Recall,

(20.20)

or,

(20.21)

The efficiency of no heat engine can be greater than one. The lowest possible temperature in this scale is zero .

Figure 20.2

Refer to Figure 20.2. Hence it is called the absolute temperature scale. The absolute temperature scale is also known as Kelvin temperature scale. In defining the Kelvin temperature scale also, the triple point of water is taken as the standard reference point. For a Carnot engine operating between reservoirs at temperature and being the triple point of water arbitrarily assigned the value of ,

or,

(20.22)

If this equation is compared with the perfect gas temperature scale [remember, we have obtained where , it is seen that in the Kelvin Scale Q plays the role of the thermometric property.