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Chapter 10: Problem 90

If mass-energy equivalence is taken into account, when water is cooled to form ice, then the mass of water should \(\quad[\mathbf{2 0 0 2}]\) (A) increase. (B) remain unchanged. (C) decrease. (D) first increase then decrease.

Short Answer

Expert verified
When water cools down to form ice, its internal energy decreases as it loses heat to the environment. According to the mass-energy equivalence principle (\(E=mc^2\)), this energy decrease results in a decrease in mass. Hence, the mass of water should decrease when it cools down to form ice. The correct answer is (C) decrease.

Step by step solution

01

Identify the process#

When water cools down and turns into ice, it goes through a phase change. During this phase change, the thermal energy of the water decreases as it loses heat to the surroundings. The water molecules slow down and eventually form a solid structure, which is ice. In other words, there is an overall reduction in the internal energy of the water when it forms ice. Now, let's see how this affects its mass based on the mass-energy equivalence principle.
02

Understand mass-energy equivalence#

Mass-energy equivalence is given by the famous equation, \(E=mc^2\), where \(E\) is the energy, \(m\) is the mass, and \(c\) is the speed of light. According to this principle, energy and mass are interchangeable. Thus, when energy of a system changes, it can result in a change in its mass.
03

Apply mass-energy equivalence principle#

In the case of water cooling down to form ice, there is a decrease in internal energy as the water loses heat to the environment. As a result, the energy decrease is accompanied by a corresponding decrease in mass due to the mass-energy equivalence principle. Therefore, the mass of water should decrease when it cools down to form ice.
04

Choose the correct answer#

Having analyzed the relationship between energy and mass during the phase change of water to ice and applied the mass-energy equivalence principle, we can conclude that the mass of water should decrease. Hence, the correct answer is: (C) decrease.

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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 undergoes a phase change, it transitions from one state of matter to another. During this process, energy must be absorbed or released by the substance.
The classic example is water transitioning to ice. As water cools from a liquid to a solid state, it releases energy in the form of heat to the environment.
This release of energy occurs because the water molecules slow down, losing kinetic energy as they begin to arrange into a more orderly, solid structure.
  • Water releases latent heat during the freezing process.
  • No temperature change occurs during the phase change, only a change of state.
Recognizing how energy flow influences phase changes is key to understanding subsequent changes in the system.
Internal Energy
Internal energy encompasses all the energy contained within a substance. It is the sum of potential energy due to the interactions between particles and kinetic energy associated with the internal motion of these particles.
For a system undergoing a phase change, such as water turning to ice, there is a notable shift in internal energy. When ice forms, the potential energy decreases as the molecules become more tightly bound in an ordered structure, which reflects a lower energy state. Moreover, the kinetic energy decreases due to the lower temperatures, slowing the molecular motion.
  • The loss of internal energy primarily stems from the reduction in both kinetic and potential energy.
  • The total internal energy decreases until the water has fully transitioned to ice.
Understanding internal energy variations helps in comprehending complex thermodynamic transitions like phase changes.
Mass Change
The concept of mass change during energy transformations is rooted in the mass-energy equivalence principle, succinctly captured by the equation, \(E=mc^2\). This principle reveals that energy and mass are fundamentally connected, and a change in energy equates to a change in mass.So, what happens during a phase change like the cooling of water into ice? When water loses energy and transitions to a lower energy state, the total mass must also decrease slightly.
According to \(E=mc^2\), as the system loses energy, it loses a corresponding amount of mass, which, though very minute, is significant in theoretical calculations.
  • This mass decrease isn't perceptible under normal conditions but is crucial in precise scientific models.
  • The process highlights how interconnected mass and energy truly are in nature.
Understanding mass change during phase changes enriches our comprehension of natural laws and the universe.

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Most popular questions from this chapter

A copper plate of length \(1 \mathrm{~m}\) is riveted to two steel plates of same length and same cross-section area at \(0^{\circ} \mathrm{C}\). Calculate tension (in kilo newton) generated in copper plate when heated to \(20^{\circ} \mathrm{C}\). \(Y_{\text {copper }}=\frac{1}{2} \times Y_{\text {steel }}=2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2} Y=\) Young's modules \(\alpha_{\text {copper }}=18 \times 10^{-6} \mathrm{~K}^{-1}\) \(\alpha_{\text {steel }}=11 \times 10^{-6} \mathrm{~K}^{-1} \alpha=\) coefficient of linear expansion Area of each plate \(=50 \mathrm{~cm}^{2}\)

Heat is associated with, (A) Kinetic energy of random motion of molecules. (B) Kinetic energy of orderly motion of molecules. (C) Total kinetic energy of random and orderly motion of molecules. (D) Kinetic energy of random motion in some cases and kinetic energy of orderly motion in other.

Two liquids \(A\) and \(B\) are at \(32^{\circ} \mathrm{C}\) and \(24^{\circ} \mathrm{C}\). When mixed in equal masses, the temperature of the mixture is found to be \(28^{\circ} \mathrm{C}\). Their specific heats are in the ratio of (A) \(3: 2\) (B) \(2: 3\) (C) \(1: 1\) (D) \(4: 3\)

An inflated rubber balloon contains 1 mole of an ideal gas, has a pressure \(p\), volume \(V\), and temperature \(T\). If the temperature rises to \(1.1 T\), and the volume is increased to \(1.05 \mathrm{~V}\), the final pressure will be (A) \(1.1 p\) (B) \(p\) (C) less than \(p\) (D) between \(p\) and \(1.1\)

A cylinder containing an ideal gas is in vertical position and has a piston of mass \(M\) that is able to move up or down without friction (Fig. \(10.19\) ). If the temperature is increased. (A) Both \(p\) and \(V\) of the gas will change (B) Only \(p\) will increase according to Charles' law (C) \(V\) will change but \(\operatorname{not} p\) (D) \(p\) will change but not \(V\)
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