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Chapter 15: Problem 23

If mass-energy equivalence is taken into account, when water is cooled to form ice, the mass of water should be (a) increase (b) remain unchanged (c) decrease (d) first increase then decrease

Short Answer

Expert verified
The mass of water should decrease (option c).

Step by step solution

01

Understand Mass-Energy Equivalence

According to Einstein's mass-energy equivalence principle, represented by the equation \(E=mc^2\), energy and mass are interchangeable. The equation shows that a change in the energy of a system affects its mass.
02

Analyze the Process of Cooling Water

When water is cooled to form ice, it releases energy in the form of heat to the surroundings. This release of energy implies a decrease in the internal energy of the system (water turning into ice).
03

Apply Mass-Energy Equivalence to Cooling

Due to the energy release during the cooling process, according to \(E=mc^2\), there is a reduction in energy, which results in a decrease of mass. The mass must reduce as the system loses energy to the surroundings.
04

Choose the Correct Answer

Based on the understanding that a reduction in energy results in a decrease in mass, the correct option for the mass of water when it freezes with energy loss is (c) decrease.

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Key Concepts

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

Mass Change
When water is cooled to form ice, a fascinating transformation takes place, involving a concept known as mass change. This change refers to the decrease in mass as the system loses energy. It might sound a bit puzzling that mass could change in this way, but it's all tied to what happens on an atomic level.

As water cools and freezes, it releases energy (think of it like shedding a layer). This energy reduction affects the mass of the entire system. So, as energy departs from the water, the mass of the water also slightly decreases. This is because energy and mass are deeply connected.
  • Mass change occurs as a result of energy transitions.
  • Even though this mass change is minuscule, it's real and significant from a scientific perspective.
Energy Release
During the cooling process, one key aspect is the energy release. When liquid water turns into ice, it must lose energy to stabilize and form solid structures. This loss is expressed as heat energy moving away to the surrounding environment.

It's similar to how you might feel after strenuous exercise; you release energy (or heat) into your surroundings, cooling your body down. In the water to ice scenario, this released energy is what allows water molecules to order themselves into a solid form, known as ice.
  • Energy is released in the form of heat.
  • This energy loss is linked to the cooling down and freezing of water.
Cooling Process
Understanding the cooling process helps illuminate how energy transitions result in phase changes, such as water turning to ice.

When water is cooled, the kinetic energy of water molecules decreases, which results in a slower movement. As molecules slow down, they organize into a fixed position, forming a crystalline structure. This organization marks the transition from liquid to solid.
  • Cooling is necessary for water to freeze into ice.
  • Energy loss leads to decreased motion, allowing for the formation of ice.
Einstein's Equation
At the heart of these phenomena is Einstein鈥檚 equation, a pivotal concept that links energy and mass. This groundbreaking formula, expressed as \(E=mc^2\), where \(E\) represents energy, \(m\) is mass, and \(c\) is the speed of light, shows how energy and mass are interchangeable.

In the context of water freezing, it's this equation that explains why mass decreases as energy is released. The mass lost is incredibly small, too tiny to measure with everyday tools, but it's a crucial concept in physics.
  • Einstein鈥檚 equation provides the foundation for mass-energy equivalence.
  • This principle is essential for understanding processes like freezing, where energy transformations impact mass.

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Most popular questions from this chapter

What extinguishes a fire most quickly? (a) Cold water (b) Boiling water (c) Hot water (d) Ice

A cylinder of radius \(R\) made of a material of thermal conductivity \(K_{1}\) is surrounded by a cylindrical shell of inner radius \(R\) and outer radius \(2 R\) made of a material of thermal conductivity \(K_{2}\). The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is: (a) \(K_{1}+K_{2}\) (b) \(\frac{K_{1}+3 K_{2}}{4}\) (c) \(\frac{K_{1} K_{2}}{K_{1}+K_{2}}\) (d) \(\frac{3 K_{1}+K_{2}}{4}\)

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