Heat and Work

Energy can move into or out of a system in different ways. Two of the most important energy-transfer processes in thermodynamics are heating and work.

The key idea is:

Heat and work are ways of transferring energy. They are not substances stored inside an object.

An object can store energy as internal energy, but energy can be transferred into or out of that internal energy store by heating or by doing work.

Heat as an Energy Transfer

In everyday language, we often say that an object "contains heat." In physics, it is more accurate to describe heating as a transfer of energy caused by a temperature difference.

If two objects at different temperatures interact, energy tends to transfer:

from the higher-temperature object → to the lower-temperature object

For example, place a hot metal block into cool water.

Energy transfers from the metal to the water.

As a result:

• the metal loses internal energy
• the water gains internal energy
• the metal cools
• the water warms

Eventually, they may reach the same temperature.

At that point there is no net energy transfer by heating between them.

Heat and Temperature Are Different

Temperature tells us about the thermal state of a system and is related to the average kinetic energy of its particles.

Heating describes energy being transferred because of a temperature difference.

They are therefore not the same thing.

For example, when a pan is placed on a hot stove:

• the stove has a higher temperature
• energy is transferred to the pan by heating
• the internal energy of the pan increases
• the temperature of the pan usually rises

How Energy Is Transferred by Heating

Energy can be transferred because of temperature differences through several mechanisms.

Conduction

Conduction occurs through interactions between neighbouring particles.

For example, when one end of a metal rod is heated, particles in that region vibrate more vigorously. Energy is transferred through the material.

Metals are particularly good thermal conductors.

Convection

Convection occurs in fluids such as liquids and gases through the movement of the fluid.

Warmer, less dense regions may rise while cooler, denser regions sink, producing convection currents.

Thermal Radiation

Energy can also be transferred by electromagnetic radiation, especially infrared radiation.

Unlike conduction and convection, radiation does not require matter and can travel through a vacuum.

Energy from the Sun reaches Earth mainly by radiation.

Work as an Energy Transfer

Work is another way energy can be transferred.

Mechanical work occurs when a force causes displacement.

For a constant force acting in the direction of motion:

W = Fd

where:

• W = work done in joules (J)
• F = force in newtons (N)
• d = displacement in metres (m)

If you push a box across the floor, you do work on the box.

Energy is transferred from you to the box and its surroundings.

Work and Internal Energy

Work can also change the internal energy of a system.

A useful example is compressing a gas.

Imagine air inside a cylinder fitted with a movable piston.

If you push the piston inward:

• you exert a force
• the piston moves
• work is done on the gas
• energy is transferred into the gas
• the internal energy of the gas can increase

The gas may therefore become warmer.

This demonstrates that internal energy can change without energy being transferred by heating.

Compression of a Gas

Suppose a gas is trapped inside a cylinder.

When the piston is pushed inward, the gas is compressed.

The surroundings do work on the gas.

Energy is transferred into the gas's internal energy store.

If little energy escapes to the surroundings:

compression → internal energy increases → temperature increases

This is why a bicycle pump can become warm when air is compressed repeatedly.

Expansion of a Gas

The reverse process occurs when a gas expands against an external pressure.

Imagine a gas pushing a piston outward.

The gas exerts a force on the piston, and the piston moves.

Therefore, the gas does work on its surroundings.

Energy is transferred from the gas to the surroundings.

If this energy is not replaced by heating:

expansion → internal energy decreases → temperature may decrease

Work Done by an Expanding Gas

For a gas expanding against a constant external pressure, the work done by the gas can be calculated using:

W = pΔV

where:

• W = work done by the gas in joules (J)
• p = external pressure in pascals (Pa)
• ΔV = change in volume in cubic metres (m³)

The change in volume is:

ΔV = V₂ − V₁

where:

• V₁ = initial volume
• V₂ = final volume

For expansion:

V₂ > V₁

so ΔV is positive.

Why W = pΔV?

Consider a gas pushing a piston of area A through a distance d.

Mechanical work is:

W = Fd

Pressure is:

p = F/A

so:

F = pA

Substitute this into the work equation:

W = pAd

But:

Ad = ΔV

because the piston area multiplied by the distance moved gives the change in volume.

Therefore:

W = pΔV

This connects ordinary mechanical work with the work done by an expanding gas.

Worked Example: Expanding Gas

A gas expands from 0.020 m³ to 0.035 m³ against a constant pressure of 100,000 Pa.

First calculate the change in volume:

ΔV = V₂ − V₁

ΔV = 0.035 − 0.020

ΔV = 0.015 m³

Now calculate the work:

W = pΔV

W = 100000 × 0.015

W = 1500 J

The gas does:

1,500 J of work on its surroundings.

This means 1,500 J of energy has been transferred from the gas through mechanical work.

Another Worked Example

A gas expands from 2.0 × 10⁻³ m³ to 5.0 × 10⁻³ m³ against a constant external pressure of 2.0 × 10⁵ Pa.

Calculate the volume change:

ΔV = 5.0 × 10⁻³ − 2.0 × 10⁻³

ΔV = 3.0 × 10⁻³ m³

Now:

W = pΔV

W = (2.0 × 10⁵)(3.0 × 10⁻³)

W = 600 J

Therefore, the gas transfers 600 J of energy to its surroundings by doing work.

Unit Check

The pressure-volume equation produces joules because:

1 Pa = 1 N/m²

Therefore:

Pa × m³ = (N/m²)(m³)

= N·m

and:

1 N·m = 1 J

So:

Pa·m³ = J

This is useful for checking that the units in a calculation are correct.

Be Careful with Volume Units

Gas volumes are often given in litres, but pressure is commonly measured in pascals.

When using:

W = pΔV

volume should normally be converted to m³.

Remember:

1 m³ = 1000 L

Therefore:

1 L = 0.001 m³

or:

1 L = 1 × 10⁻³ m³

Example

A gas expands by 4.0 L.

Convert to cubic metres:

4.0 L × 0.001 = 0.0040 m³

If the pressure is 150,000 Pa:

W = 150000 × 0.0040

W = 600 J

Expansion vs. Compression

It is useful to distinguish who is doing the work.

Gas Expands

The gas pushes the surroundings.

The gas does work on the surroundings.

Energy is transferred out of the gas by work.

Gas Is Compressed

The surroundings push the gas.

Work is done on the gas.

Energy is transferred into the gas by work.

This distinction becomes important when analysing changes in internal energy.

Heat and Work Together

A system can experience both heating and work at the same time.

Consider a gas in a cylinder being heated.

Energy is transferred into the gas by heating.

As the gas expands, it pushes the piston.

Energy is transferred out of the gas by work.

The change in internal energy depends on the balance between these transfers.

For example, suppose:

• 900 J is transferred into a gas by heating
• the gas does 350 J of work on its surroundings

The remaining energy increases the gas's internal energy:

ΔU = 900 − 350

ΔU = 550 J

The internal energy increases by 550 J.

Energy Accounting

A useful way to think about thermodynamics is as energy accounting.

Energy entering a system must either:

• increase an energy store, or
• leave the system through another transfer pathway

Suppose 2,000 J is transferred into a gas by heating and the gas does 800 J of work.

Then:

Energy in = 2000 J

Energy out by work = 800 J

Increase in internal energy:

2000 − 800 = 1200 J

Energy is conserved throughout the process.

Identifying Heat and Work in Everyday Situations

Hot Drink Cooling

Energy transfers from the drink to the surroundings because of a temperature difference.

Main process: heating

Bicycle Pump

You push the piston and compress the gas.

Main process: work done on the gas

Gas Expanding Against a Piston

The gas pushes the piston outward.

Main process: work done by the gas

Metal Spoon in Hot Soup

Energy transfers from the hotter soup into the cooler spoon.

Main process: heating

Rubbing Your Hands Together

Forces act through distances, and mechanical energy is ultimately transferred into internal energy.

Work contributes to increasing internal energy.

Heating Gas That Expands

Energy enters by heating while energy also leaves as the gas does work.

Both heating and work are involved.

Heat and Work Are Not Stored

This is an important thermodynamic distinction.

A system can possess:

• internal energy
• kinetic energy
• gravitational potential energy
• other energy stores

But heat and work describe energy being transferred across the boundary of a system.

Once the transfer has occurred, we describe the resulting change in the system's energy rather than saying that the system "stores work" or "stores heat."

Real-World Applications

Internal Combustion Engines

Hot gases expand inside an engine cylinder and do work on a piston. This transfers energy from the gas into mechanical motion.

Steam Turbines

High-pressure steam expands and transfers energy by doing work on turbine blades.

Refrigerators

A refrigerant is repeatedly compressed and expanded. Work and heating processes allow energy to be transferred from inside the refrigerator to the surroundings.

Air Compressors

Mechanical work is done on a gas during compression, which can significantly increase its temperature.

Power Stations

Many power stations use heating to increase the internal energy of a working fluid, which then expands and performs mechanical work.

Common Mistakes

Thinking heat is stored inside an object

Internal energy is stored. Heating describes an energy transfer caused by a temperature difference.

Thinking temperature is heat

Temperature and heating are different concepts. Temperature describes the thermal state of a system; heating describes energy transfer.

Forgetting who does the work

During expansion, the gas does work on the surroundings.

During compression, the surroundings do work on the gas.

Using litres directly in W = pΔV

If pressure is measured in pascals, convert litres to cubic metres.

Using the final volume instead of the change in volume

Use:

ΔV = V₂ − V₁

not simply V₂.

Assuming all energy transferred by heating increases internal energy

If a gas expands, some energy may leave the system as work.

Key Terms

Heating — transfer of energy caused by a temperature difference.

Work — transfer of energy when a force acts through a displacement or through processes such as gas compression and expansion.

Internal energy — the total microscopic kinetic and potential energy of the particles in a system.

System — the object or collection of matter being studied.

Surroundings — everything outside the system that can interact with it.

System boundary — the dividing surface between a system and its surroundings.

Conduction — energy transfer through particle interactions within or between materials.

Convection — energy transfer involving bulk movement of a fluid.

Thermal radiation — transfer of energy by electromagnetic radiation.

Expansion — an increase in the volume of a gas.

Compression — a decrease in the volume of a gas.

Pressure — force per unit area.

Volume change — the difference between final and initial volume: ΔV = V₂ − V₁.

Work done by a gas — energy transferred from a gas when it expands against an external pressure.

Key Takeaways

• Heat and work are energy-transfer processes.
• Heating occurs because of a temperature difference.
• Work transfers energy through forces and displacement.
• Heating and work can both change the internal energy of a system.
• Compressing a gas involves work being done on the gas.
• An expanding gas can do work on its surroundings.
• For constant external pressure, work done by an expanding gas can be calculated using W = pΔV.
• Pressure should be in Pa and volume change in m³ to obtain work in joules.
• 1 L = 1 × 10⁻³ m³.
• A gas can receive energy by heating while simultaneously transferring energy away by doing work.
• Energy conservation allows us to account for changes in internal energy.
• Identifying the system and surroundings makes heat-and-work problems easier to understand.

Check Your Understanding

1. Explain the difference between internal energy and heating.
2. In which direction does energy transfer by heating between objects at different temperatures?
3. Give one example of energy transfer by conduction, convection, and radiation.
4. Explain how doing work on a gas can increase its internal energy.
5. Why can a bicycle pump become warm when air is compressed?
6. A gas expands from 0.030 m³ to 0.050 m³ against a pressure of 80,000 Pa. Calculate the work done by the gas.
7. A gas expands by 6.0 L against a constant pressure of 120,000 Pa. Calculate the work done.
8. A gas expands from 3.0 × 10⁻³ m³ to 8.0 × 10⁻³ m³ against a pressure of 2.5 × 10⁵ Pa. Calculate the work done.
9. A gas receives 1,400 J of energy by heating and does 500 J of work on its surroundings. By how much does its internal energy increase?
10. A gas receives 2,500 J by heating while doing 1,800 J of work. Calculate its change in internal energy.
11. Explain why W = pV would generally be incorrect for calculating the work done during an expansion.
12. A student says, "The gas contains 500 J of heat." Explain why this statement is not an accurate thermodynamic description.