Chapter 8, Problem 1P

To determine

Whether the temperature in the Clausius inequality relation have to be absolute temperature. And why?

Explanation of Solution

Clausius inequality relation:

For any system, the cyclic integral of $\delta Q/T$ is always less than or equal to zero. The mathematical expression of Clausius inequality is expressed as follows:

  ${\displaystyle \oint \frac{\delta Q}{T}}\le 0$        (I)

Here, $\delta Q$ is the differential amount of heat transfer from or to a system, and $T$ is absolute temperature.

Absolute temperature:

The temperature of an object or a system is measured on a scale where zero is taken as absolute zero. It is also called as thermodynamic temperature. The common absolute temperature scales are as follows:

• Kelvin temperature scale
• Rankine temperature scale

The temperature when the atoms and molecules of the system have zero kinetic energy is known as absolute zero temperature.

From Equation (I),

It is clear that the Clausius inequality relation is valid when the temperature is measured in absolute scale.

Thus, it is necessary that the temperature in the Clausius inequality relation have to be absolute temperature.