Chapter 16, Problem 1FTD

If system A is not in thermodynamic equilibrium with system B, and B is not in equilibrium with C, can you draw any conclusions about the temperatures of the three systems?

To determine

Conclusions about the temperature of three system, If system $A$ is not in thermodynamic equilibrium with system $B$, and $B$ is not in equilibrium with $C$.

Answer to Problem 1FTD

The temperature of $A$ and $C$ can be either same or different depending on whether they are in thermal equilibrium or not but temperature of $B$ is not equal to $A$ and $C$ because they are no tin thermal equilibrium.

Explanation of Solution

Zeroth law of thermodynamics states that if a system $A$ is in thermodynamic equilibrium with $B$ and the system $B$ is in thermodynamic equilibrium with $C$ then $A$ and $C$ are in thermal equilibrium and the temperature of all the three system are same.

But if systems $A$ and $B$ are not in thermal equilibrium then their temperature might be different, If the systems $B$ and $C$ are in thermal equilibrium then their temperature might be different. But there is a possibility that system $A$ and $C$ are in thermodynamic equilibrium. If they are in equilibrium their temperature remain same and if not temperature also be different.

Therefore the temperature of $A$ and $B$ are different, $B$ and $C$ are different and between $A$ and $C$ can be either same or different.

Conclusion:

Thus, the temperature of $A$ and $C$ can be either same or different depending on whether they are in thermal equilibrium or not but temperature of $B$ is not equal to $A$ and $C$ because they are no tin thermal equilibrium.