Question

The law of conscrvation of energy states that (1) the internal energy of a system is constant (2) the heat content of the system is constant (3) cnergy is neither created nor destroyed (4) there is an equivalence between energy and mass

Short answer

Option 3: energy is neither created nor destroyed.

Step-by-step solution

Understand the Concept

The law of conservation of energy is a fundamental principle in physics. This law states that energy in an isolated system remains constant over time.

Analyze the Options

Review the given options to determine which one accurately reflects the concept of energy conservation.

Evaluate Option 1

Option 1 states that the internal energy of a system is constant. This is not always true as internal energy can change due to work or heat transfer.

Evaluate Option 2

Option 2 states that the heat content of the system is constant. This is incorrect as heat content can vary with energy transfer processes.

Evaluate Option 3

Option 3 states that energy is neither created nor destroyed, aligning directly with the law of conservation of energy.

Evaluate Option 4

Option 4 suggests an equivalence between energy and mass, which relates to Einstein's theory of relativity, not the conservation of energy.

Select the Correct Answer

Based on the evaluation, the answer is Option 3: energy is neither created nor destroyed.

Key concepts

energy conservation

The law of energy conservation is a vital principle in physics. It states that within an isolated system, the total energy remains constant over time. This means that energy can change form, like turning from kinetic to potential energy, but the total amount stays the same.
Think of a roller coaster: it has maximum kinetic energy at the lowest points and maximum potential energy at the highest points. The sum of kinetic and potential energy, however, does not change.

isolated system

An isolated system is a physical system with no interaction with its surroundings. This means no matter or energy can enter or leave.
For example:

• A perfectly insulated container where no heat can transfer in or out.
• A sealed thermos bottle.

In these scenarios, the total energy inside the system remains the same, allowing us to apply the law of conservation of energy accurately. When a system is isolated, it's easier to track energy changes within it.

internal energy

Internal energy refers to the total energy contained within a system. It includes kinetic energy from the motion of particles and potential energy from the forces between them.
Understanding this concept is key in thermodynamics. Changes in internal energy occur via heat transfer or performing work. Thermal vibrations of molecules contribute to internal energy. Unlike the scenario in the exercise, internal energy isn't always constant; various processes can alter it.

heat transfer

Heat transfer is the movement of thermal energy from one object or material to another. This process occurs because of a temperature difference. There are three main types:

• Conduction: Direct transfer through material, like a hot stove heating a pot.
• Convection: Transfer through fluid motion, such as boiling water.
• Radiation: Transfer through electromagnetic waves, like sunlight warming your skin.

Understanding these processes helps us see how energy can move and change form within a system, impacting its internal energy.

Einstein's theory of relativity

Einstein's theory of relativity introduces a groundbreaking idea: energy and mass are interchangeable. This relationship is famously captured in the equation \(E = mc^2\). Here, \(E\) represents energy, \(m\) is mass, and \(c\) is the speed of light.
This principle explains how massive stars convert mass into vast amounts of energy. Although connected, this concept is distinct from the law of conservation of energy. While conservation focuses on energy constancy in an isolated system, relativity explores the deep connection and equivalence between energy and mass.