CALC You decide to take a nice hot bath but discover that your thoughtless roommate has used up most of the hot water. You fill the tub with 195 kg of 30.0°C water and attempt to warm it further by pouring in 5.00 kg of boiling water from the stove. (a) Is this a reversible or an irreversible process? Use physical reasoning to explain.

Verified step by step guidance

1. Identify the initial temperatures of the two water masses. The 195 kg of water is at 30.0°C, and the 5.00 kg of boiling water is at 100°C.
2. Understand that heat transfer will occur between the two masses of water until thermal equilibrium is reached, meaning both masses will eventually have the same temperature.
3. Recognize that this process involves heat transfer without any external work being done or heat being added from an external source, which typically characterizes an irreversible process.
4. Consider the second law of thermodynamics, which states that entropy of an isolated system always increases for irreversible processes. In this scenario, the mixing of two different temperatures results in an increase in entropy.
5. Conclude that the process is irreversible because once the heat has transferred and the waters have mixed, you cannot separate them back into their original masses with the original temperatures without expending additional energy.

Key Concepts

Reversible and Irreversible Processes

In thermodynamics, a reversible process is one that can be reversed without leaving any change in the system or surroundings, while an irreversible process cannot be reversed without some change occurring. The mixing of hot and cold water is typically irreversible because it leads to a uniform temperature distribution, and energy is dissipated as heat, making it impossible to return to the original states without external work.

Heat Transfer

Heat transfer is the process of thermal energy moving from a hotter object to a cooler one until thermal equilibrium is reached. In this scenario, when boiling water is added to the cooler water, heat flows from the boiling water to the cooler water, raising the overall temperature of the mixture. This process is governed by the principles of conduction and convection.

Thermal Equilibrium

Thermal equilibrium occurs when two objects in thermal contact no longer exchange heat, meaning they are at the same temperature. In the context of the bath scenario, once the boiling water is added, the system will eventually reach thermal equilibrium, where the temperature of the mixed water stabilizes. This concept is crucial for understanding how energy is distributed in the system.