Question

A cup of tea placed in the room eventually acquires a room temperature by losing heat. The process may be considered close to (1) cyclic process (2) reversible process (3) isothermal process (4) zeroth law

Short answer

Zeroth Law

Step-by-step solution

Identify the Nature of the Process

We are given a scenario where a cup of tea loses heat to eventually match the room temperature. Understanding the nature of the process is critical here.

Evaluate the Cyclic Process

A cyclic process is one where the system returns to its initial state after completing a cycle. In this case, the cup of tea does not return to its initial state after losing heat, so this cannot be classified as a cyclic process.

Evaluate the Reversible Process

A reversible process means the system can return to its initial state with no entropy change in the overall system. Losing heat to the room irreversibly increases the entropy, hence this is not a reversible process.

Evaluate the Isothermal Process

An isothermal process involves the system remaining at the same temperature. Since the cup of tea starts at a higher temperature and gradually cools to room temperature, it is not an isothermal process.

Evaluate the Zeroth Law

The Zeroth Law of Thermodynamics states that when two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other. The cup of tea reaching thermal equilibrium with the room temperature is an illustration of this law in action.

Conclusion

Given the options and the reasoning, the cup of tea cooling down to room temperature can best be associated with the Zeroth Law of Thermodynamics.

Key concepts

cyclic process

A cyclic process is a series of thermodynamic steps that return a system to its original state. Think of an engine, where the working fluid undergoes various transformations, but ultimately, it returns to its initial conditions. In these processes, which often involve changes in pressure, volume, and temperature, the key feature is repeatability. Systems undergo sequential states but come back to the starting point, allowing the cycle to repeat.

However, in the case of the cooling tea, the system (tea) isn't returning to its original hot state after reaching room temperature. Instead, the tea progressively loses heat and settles at room temperature, making it a non-cyclic process.

reversible process

A reversible process is one in which the system and its surroundings can be restored to their initial states with no net change in entropy. These processes are idealized and occur infinitely slowly to ensure equilibrium at every stage.

Consider a piston with gas inside, slowly compressing and decompressing without generating extra heat or causing irreversible changes.

When a cup of tea cools to room temperature, it loses heat irreversibly, usually accompanied by entropy increase in the surroundings. For an everyday scenario, especially with heat transfer to the environment, the process tends to be irreversible, explaining why cooling tea isn't reversible.

isothermal process

An isothermal process maintains a constant temperature throughout the system's transformation. This kind of process often happens when the system is in perfect thermal contact with an external reservoir, exchanging heat precisely to keep the temperature steady.

For example, when a gas expands or contracts while maintaining a steady temperature by absorbing or releasing heat to the surroundings, it undergoes an isothermal transformation. On the contrary, when tea loses heat and cools to match room temperature, the temperature of the tea decreases steadily. Thus, it is not isothermal.

zeroth law of thermodynamics

The Zeroth Law of Thermodynamics establishes the basis for measuring temperature. It states that if two systems are each in thermal equilibrium with a third system, they are also in thermal equilibrium with each other.

In simpler terms, if object A is in thermal equilibrium with object B, and object B is in thermal equilibrium with object C, then object A and object C are in thermal equilibrium. In the context of our exercise, the cup of tea reaches thermal equilibrium with the room's air. This gradual heat transfer until both have the same temperature illustrates the Zeroth Law in action.

By this process, we understand why the cup of tea achieving room temperature is associated with the Zeroth Law of Thermodynamics.