If 0.45 kg of water at 100°C is changed by a reversible process to steam at 100°C, determine the change in entropy of the universe as a whole.

검증된 단계별 안내

Identify the key concept: The problem involves a phase change (water to steam) at constant temperature, which is an isothermal process. The change in entropy of the universe is the sum of the entropy changes of the system (water) and the surroundings.

Calculate the entropy change of the system (water): Use the formula \( \Delta S_{\text{system}} = \frac{Q}{T} \), where \( Q \) is the heat absorbed during the phase change and \( T \) is the absolute temperature. The heat \( Q \) can be calculated using \( Q = mL \), where \( m \) is the mass of the water and \( L \) is the latent heat of vaporization of water.

Substitute the known values: \( m = 0.45 \; \text{kg} \), \( L = 2.26 \times 10^6 \; \text{J/kg} \), and \( T = 100 + 273.15 = 373.15 \; \text{K} \). Compute \( Q \) and then use it to find \( \Delta S_{\text{system}} \).

Determine the entropy change of the surroundings: Since the process is reversible, the heat lost by the surroundings is equal in magnitude but opposite in sign to the heat gained by the system. Thus, \( \Delta S_{\text{surroundings}} = -\frac{Q}{T} \), where \( T \) is the same temperature as the system.

Add the entropy changes: The total entropy change of the universe is \( \Delta S_{\text{universe}} = \Delta S_{\text{system}} + \Delta S_{\text{surroundings}} \). For a reversible process, these two terms cancel out, resulting in \( \Delta S_{\text{universe}} = 0 \).

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Entropy

Entropy is a measure of the disorder or randomness in a system. In thermodynamics, it quantifies the amount of energy in a system that is not available to do work. When a substance undergoes a phase change, such as from water to steam, the entropy of the system increases due to the greater disorder in the gaseous state compared to the liquid state.

Reversible Process

A reversible process is an idealized process that occurs in such a way that the system and its surroundings can be returned to their original states without any net change. In thermodynamics, reversible processes are characterized by equilibrium at every stage, allowing for maximum efficiency and the ability to calculate changes in state variables, such as entropy, accurately.

Change in Entropy of the Universe

The change in entropy of the universe is the sum of the changes in entropy of the system and its surroundings. According to the second law of thermodynamics, the total entropy of the universe tends to increase over time. In the context of the given problem, calculating the change in entropy involves considering both the entropy change of the water turning into steam and the heat exchanged with the surroundings during the process.