Chapter 7.13, Problem 1P

To determine

Whether the temperature in the Clausius inequality relation has to be absolute temperature.

Explanation of Solution

According to the Clausius inequality, the cyclic integral of ${\displaystyle \oint \frac{\delta Q}{T}}$ is always less than or equal to zero.

Write the Clausius inequality equation.

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

Here, the heat given or rejected from the system is $\delta Q$ and the absolute temperature of the system is $T$.

Write the equation for the reversible heat engine.

$\frac{Q_H}{T_H}=\frac{Q_L}{T_L}$ (I)

Here, the heat extracted from the source is $Q_H$, the absolute temperature of the source is $T_H$, the heat given to the sink is $Q_L$ and the absolute temperature of the sink is $T_L$.

The Clausius inequality equation is derived from Equation (I). Thus, the temperature in the Clausius inequality relation has to be absolute temperature.