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Two kilograms of water are changed (a) from ice at \(0^{\circ} \mathrm{C}\) into liquid water at \(0^{\circ} \mathrm{C}\) and \((\mathbf{b})\) from liquid water at \(100^{\circ} \mathrm{C}\) into steam at \(100^{\circ} \mathrm{C}\). For each situation, determine the change in mass of the water.

Short Answer

Expert verified
The change in mass is 0 kg for both scenarios.

Step by step solution

01

Understand the Problem

We are given two scenarios involving the phase change of water. In both cases, the mass of water is initially 2 kg, and we need to calculate the change in mass after phase changes: (a) ice to liquid water at 0°C, and (b) liquid water to steam at 100°C.
02

Recall the Law of Conservation of Mass

According to the law of conservation of mass, the mass of a closed system must remain constant over time, as it is not possible to create or destroy mass in an isolated system.
03

Analyze Scenario (a) Ice to Liquid Water

In scenario (a), ice at 0°C is converted into liquid water at 0°C. The process is a phase change from solid to liquid. Given that no material is added or lost, the mass remains the same. Thus, the change in mass is 0 kg.
04

Analyze Scenario (b) Liquid Water to Steam

In scenario (b), liquid water at 100°C is converted into steam at 100°C. This is a phase change from liquid to gas. Similarly, no addition or loss of material occurs, so the mass remains constant. Thus, the change in mass is 0 kg.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Phase Change
Phase change is a fundamental scientific concept where matter changes from one state to another. The states, or phases, typically include solid, liquid, and gas. For example, ice turning into water and water turning into steam represent phase changes.

During a phase change, energy is either absorbed or released, but it doesn't result in any change in mass within a closed system. This is because a phase change only alters the state of the substance, not the amount of substance itself.

It’s fascinating to note how this simple process of altering states involves impactful processes at the molecular level. Ice melting into water involves molecules gaining enough energy to break out of their rigid structure. Conversely, water turning into steam involves molecules gaining enough kinetic energy to spread out and move freely.
water properties
Water is a unique substance with special properties that make it vital for life on Earth. One of the most interesting aspects of water is its ability to exist in all three states (ice, liquid, and steam) within relatively short temperature ranges found on Earth.

With its high specific heat, water can absorb or release substantial amounts of heat without significant changes in temperature. This property plays a crucial role during phase changes:
  • When ice melts, it absorbs heat energy but stays at 0°C until entirely transformed into water.
  • Similarly, when water boils, it requires heat to turn into steam, with temperature holding constant at 100°C until the process is complete.
This persistence at specific temperatures during phase changes is known as latent heat, indicating water’s ability to consume or release energy to facilitate the phase transition, without altering its mass.
mass calculation
Mass calculation in the context of phase changes involves understanding the law of conservation of mass. According to this principle, the mass in a closed system remains constant over time. Therefore, during a phase change, even though the state may change, the total mass does not.

In the given exercise, we are dealing with water going through phase changes:
  • Ice at 0°C turning into water at 0°C.
  • Liquid water at 100°C converting into steam at 100°C.
In both scenarios, even though water transforms between solid, liquid, and gas phases, the mass remains at 2 kg.

This principle highlights an important concept in physics: whilst energy changes during phase transitions can be significant, mass itself remains unchanged, reiterating the stability and predictability of physical systems.

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