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. Step 1: Understand the concept of reversible and irreversible processes. A reversible process is one where the system and its surroundings can be returned to their original states without any changes. An irreversible process involves changes that cannot be undone without leaving a trace on the surroundings.
2. Step 2: Consider the mixing of hot and cold water. When you mix boiling water with cooler water, the temperature of the water changes, and heat is transferred from the hot water to the cooler water.
3. Step 3: Evaluate the energy exchange. In this scenario, the energy exchange between the hot and cold water leads to an increase in entropy, which is a measure of disorder. This increase in entropy is a key indicator of an irreversible process.
4. Step 4: Consider the practical aspects. In reality, once the hot water is mixed with the cooler water, it is impossible to separate them and return them to their original temperatures without external intervention, such as using a refrigerator or heater.
5. Step 5: Conclude based on physical reasoning. Since the mixing of hot and cold water results in an increase in entropy and cannot be undone without external work, this process is irreversible.

Key Concepts

Reversible and Irreversible Processes

In thermodynamics, a reversible process is one where the system and surroundings can be returned to their original states without any net change. An irreversible process involves changes that cannot be undone without leaving a net effect on the system or surroundings. Mixing hot and cold water is typically irreversible due to entropy increase and energy dissipation.

Entropy

Entropy is a measure of disorder or randomness in a system. In irreversible processes, entropy tends to increase, reflecting the natural tendency towards disorder. When hot water is mixed with cold water, the entropy of the system increases as the temperature difference equalizes, making the process irreversible.

Heat Transfer

Heat transfer is the movement of thermal energy from one object or substance to another due to temperature difference. In this scenario, heat is transferred from the boiling water to the cooler bath water, raising its temperature. The process involves conduction and results in energy distribution until thermal equilibrium is reached.