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Chapter 26: Problem 33

Phase changes require energy in the form of latent heat (Chapter 11). (a) If \(1 \mathrm{~kg}\) of ice at \(0{ }^{\circ} \mathrm{C}\) is converted to water at \(0^{\circ} \mathrm{C}\), will the water have (1) more, (2) the same, or (3) less mass compared to the ice? Why? (b) What is the difference in mass between the ice and the water? Do you think this difference would be detectable?

Short Answer

Expert verified
The mass of water is the same as that of ice (no change in mass). There is no detectable difference in mass.

Step by step solution

01

Understand the Concept of Phase Change

Phase changes, such as from ice to water, require energy input without a change in temperature. This energy, known as latent heat, is used to break molecular bonds rather than increase temperature.
02

Review Mass Conservation in Phase Change

Mass is conserved during a phase change. Therefore, the mass of ice before melting is equal to the mass of the water after melting. This means that converting ice to water at the same temperature does not change the mass.
03

Analyze the Mass Difference

Since mass is conserved during phase changes, the mass of 1 kg of ice converted to water remains 1 kg. Thus, there is no mass difference between the ice and the water.
04

Determine Detectability of Mass Difference

Since the mass difference is zero, it is not detectable. Any measurement would show that the mass remains constant.

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Key Concepts

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

Phase Change
When a substance transitions from one state of matter to another, it undergoes what we call a phase change. This is a crucial concept when discussing changes like ice turning into water. During a phase change, energy is transferred in the form of latent heat. It's fascinating to understand that the temperature does not change during this process.
  • For instance, ice absorbing heat to become liquid water remains at \(0^{\, \circ} \mathrm{C}\) until fully transformed.
  • Latent heat is the energy required to break the molecular bonds holding the ice structure together, allowing it to melt.
Unlike everyday situations where heating usually raises temperature, phase changes apply energy to alter the state without temperature fluctuation. This makes them unique scenarios in thermal physics.
Mass Conservation
Mass conservation is a fundamental principle indicating that mass remains unchanged during processes, such as phase changes. In the context of ice melting into water:
  • No mass is gained or lost when transitioning between states.
  • This means that if you start with 1 kilogram of ice, you end up with 1 kilogram of water.
This concept ensures that in closed systems, matter doesn't disappear; it merely changes form. Understanding this is essential in physics, as it explains that natural processes cannot spontaneously create or destroy matter. Specifically, in phase changes, this conservation holds true and is pivotal in solving problems related to transitions like melting ice.
Ice to Water Transformation
The transformation of ice into water is a classic example of a phase change. Here, ice absorbs latent heat to become liquid at the same temperature. Analyzing this perceptively:
  • The ice at \(0^{\, \circ} \mathrm{C}\) becomes water at \(0^{\, \circ} \mathrm{C}\) purely by absorbing and utilizing latent heat.
  • The water resulting from this process doesn't differ in mass, maintaining the original 1 kg mass under mass conservation principles.
This conversion might seem effortless but involves significant energy absorbed to break the ice's structured molecules into a fluid state. Recognizing that mass remains unchanged highlights the elegance of nature's balance and the unchanging nature of matter during phase changes.

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Most popular questions from this chapter

A boat can make a round trip between two locations, \(A\) and \(B,\) on the same side of a river in a time \(t\) if there is no current in the river. (a) If there is a constant current in the river, the time the boat takes to make the same round trip will be (1) longer, (2) the same, (3) shorter. Why? (b) If the boat can travel with a speed of \(20 \mathrm{~m} / \mathrm{s}\) in still water, the speed of the river current is \(5.0 \mathrm{~m} / \mathrm{s},\) and the distance between points A and \(B\) is \(1.0 \mathrm{~km},\) calculate the round trip times when there is no current and when there is current.

A particle of mass \(m\) is initially traveling to the right at \(0.900 c .\) It collides and sticks to a particle of mass \(2 m\) initially moving to the left at \(0.750 c\). Determine (a) the total mass (in terms of \(m\) ) of the composite particle, (b) the amount of kinetic energy lost during the collision, and (c) the velocity (speed and direction) of the composite particle.

Alpha Centauri, a star close to our solar system, is about 4.3 light-years away. Suppose a spaceship traveled this distance at a constant speed of \(0.90 c\) relative to Earth. (a) How long did the trip take according to an Earth- based clock? (b) How long did the trip take according to the traveler's clock? Which of you answers to parts (a) and (b) are proper time intervals, if any? (c) What is the trip distance according to an Earth-based observer? (d) What is the trip distance according to the traveler? Which of your answers to parts (b) and (c) are proper lengths, if any?

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Two spaceships, \(A\) and \(B\), each with a speed of \(0.60 c\) relative to Earth, approach each other head on. (a) The speed of ship A relative to ship \(B\) is (1) greater than \(c,(2)\) equal to \(c,(3)\) less than \(c\). Why? (b) What is the speed of ship A relative to ship \(\mathrm{B} ?\) (c) What is the speed of ship B relative to ship A?
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