what is the difference between work and energy?
match the words in the left column to the appropriate blanks in the sentences on the right.
reset
h
the pressure exerted as
energy is the
molecules push against a
container
work is the
change in internal energy
between the initial and final
state
capacity to do work or supply
heat
distance moved times the
force that opposes the
motion

Question

Accepted Answer

# Brief Explanations:
To solve this, we recall the definitions of energy and work in physics. Energy is defined as the capacity to do work or supply heat. Work, in the context of mechanical work (and also relevant in thermodynamics), can be related to the change in internal energy between initial and final states (or in mechanical terms, force times distance, but here the option "change in internal energy between the initial and final state" fits the thermodynamic context of work - energy relationships, and the other work - related option about force and distance might also be a mechanical work definition, but let's match based on standard definitions).

For the first blank (Energy is the...): The correct phrase is "capacity to do work or supply heat" because energy is the ability to do work or transfer heat.

For the second blank (Work is the...): The correct phrase is "change in internal energy between the initial and final state" (in thermodynamics, work done on or by a system is related to the change in internal energy, and also, the "distance moved times the force that opposes the motion" is the mechanical work formula $W = Fd$, but let's check the options. Wait, maybe I made a mistake. Wait, the option "change in internal energy between the initial and final state" is about the result of work (or heat) in thermodynamics. Wait, let's re - evaluate:

Energy definition: Energy is the capacity to do work or supply heat. So that's a standard definition.

Work: In thermodynamics, work can be the change in internal energy (when considering the first law $\Delta U=Q - W$ or $W=\Delta U - Q$ depending on sign conventions), but also, the mechanical work is force times distance. But the option "distance moved times the force that opposes the motion" is the mechanical work formula ($W = F	imes d$, where $F$ is the force opposing motion, so the work done against that force is $Fd$). Wait, maybe the intended match is:

Energy: capacity to do work or supply heat.

Work: change in internal energy between the initial and final state (or the distance - force one? Wait, let's check the options again.

The left - column options:

1. the pressure exerted as molecules push against a container: this is pressure, not related to energy or work definitions here.

2. change in internal energy between the initial and final state: this is related to work (in thermodynamics, work done on a system can change its internal energy).

3. capacity to do work or supply heat: this is the definition of energy.

4. distance moved times the force that opposes the motion: this is mechanical work ($W = Fd$).

Wait, maybe the problem has a mix of thermodynamics and mechanics. Let's get back to standard definitions:

- Energy: The ability (capacity) to do work or transfer heat. So "capacity to do work or supply heat" matches energy.

- Work: In the context of the first law of thermodynamics, work is the energy transferred when a force acts over a distance, and also, the change in internal energy can be related to work and heat. But the option "change in internal energy between the initial and final state" is a result of work (and heat) input/output. Alternatively, the mechanical work is "distance moved times the force that opposes the motion". But let's see the blanks:

First blank: Energy is the [capacity to do work or supply heat]

Second blank: Work is the [change in internal energy between the initial and final state] (or the distance - force one? Wait, maybe the problem's intended answer is:

Energy: capacity to do work or supply heat.

Work: change in internal energy between the initial and final state.

Or maybe Work is "distance moved times the force that opposes the motion". Wait, I think I need to correct. Let's use the standard definitions:

Energy: The capacity to do work or produce heat. So that's the third option.

Work: In mechanical terms, work is force times distance, which is "distance moved times the force that opposes the motion" (since work done against a force is $F	imes d$, where $F$ is the opposing force). But also, in thermodynamics, work can be associated with the change in internal energy. But given the options, let's make the correct matches:

Energy: capacity to do work or supply heat.

Work: change in internal energy between the initial and final state (or the distance - force one? Wait, maybe the problem has a typo, but based on standard definitions, the correct matches are:

Energy: capacity to do work or supply heat.

Work: change in internal energy between the initial and final state (or the distance - force one. Wait, let's check an example. Suppose we have a system. When work is done on the system, its internal energy changes. So the change in internal energy is related to work (and heat). So "change in internal energy between the initial and final state" is a result of work (and heat) transfer. So maybe that's the intended match for work.

So:

Energy is the "capacity to do work or supply heat".

Work is the "change in internal energy between the initial and final state" (or the "distance moved times the force that opposes the motion" – but let's see the options again. The option "distance moved times the force that opposes the motion" is the mechanical work formula, which is a valid definition of work. So perhaps the intended matches are:

Energy: capacity to do work or supply heat.

Work: distance moved times the force that opposes the motion.

But I think I was confused earlier. Let's re - state:

Standard definitions:

- Energy: The ability (capacity) to do work or transfer heat. So "capacity to do work or supply heat" is correct for energy.

- Work: In mechanics, work is defined as the product of the force applied and the distance moved in the direction of the force (or against the opposing force). So "distance moved times the force that opposes the motion" is the mechanical work formula ($W = F	imes d$, where $F$ is the force opposing the motion, so the work done against that force is $Fd$).

The option "change in internal energy between the initial and final state" is related to the first law of thermodynamics, where $\Delta U=Q + W$ (sign conventions vary), so the change in internal energy is the sum of heat and work. So it's not the definition of work, but a result of work (and heat) transfer.

The option "the pressure exerted as molecules push against a container" is pressure, not related to energy or work definitions here.

So the correct matches are:

Energy is the "capacity to do work or supply heat".

Work is the "distance moved times the force that opposes the motion".

Wait, but maybe the problem is from a thermodynamics perspective. Let's check a textbook. In thermodynamics, energy is the capacity to do work or transfer heat. Work is the energy transferred when a force acts over a distance, and also, the change in internal energy can be due to work (and heat). But the option "change in internal energy between the initial and final state" is about the state function, while work is a path function. Hmm. Maybe the problem has a simplified view.

Given that, let's proceed with the standard definitions:

1. Energy: capacity to do work or supply heat.

2. Work: distance moved times the force that opposes the motion (or change in internal energy? Wait, maybe the answer is:

Energy: capacity to do work or supply heat.

Work: change in internal energy between the initial and final state.

But I'm a bit confused. Let's go with the most standard definitions:

- Energy: The capacity to do work or supply heat. So that's a clear definition.

- Work: In the context of the first law of thermodynamics, work is the energy transferred that is not heat, and it can be associated with the change in internal energy. But the option "change in internal energy between the initial and final state" is a description of what work (and heat) can cause.

Alternatively, the mechanical work definition is force times distance. So the option "distance moved times the force that opposes the motion" is the mechanical work formula.

Given that, I think the intended matches are:

Energy: capacity to do work or supply heat.

Work: change in internal energy between the initial and final state.

Wait, no. Let's look for the correct definitions:

According to physics, energy is the ability to do work. So "capacity to do work or supply heat" is correct.

Work is defined as the product of force and displacement in the direction of the force, which is "distance moved times the force that opposes the motion" (since if a force $F$ opposes the motion, the work done against it is $F	imes d$).

The "change in internal energy between the initial and final state" is related to the first law of thermodynamics, where $\Delta U = Q+W$ (or other sign conventions), so it's the result of work (and heat) transfer, not the definition of work.

The "the pressure exerted as molecules push against a container" is pressure, not work or energy.

So the correct matches are:

Energy is the "capacity to do work or supply heat".

Work is the "distance moved times the force that opposes the motion".

# Answer:
Energy is the \boxed{capacity to do work or supply heat}.

Work is the \boxed{distance moved times the force that opposes the motion}.

(Note: If the intended answer for work was "change in internal energy between the initial and final state", there might be a different interpretation, but based on standard mechanical and energy definitions, the above is correct.)

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