Chapter 5 Thermodynamics

Question 1

Defining Internal Energy

Answer 1

The sum of the random distribution of kinetic and potential energies within a system of molecules

• The symbol for internal energy is U, with units of Joules (J)

Question 2

The internal energy of a system is determined by

Answer 2

• Temperature
• The random motion of molecules
• The phase of matter: gases have the highest internal energy, solids have the lowest

Question 3

The internal energy of a system can increase by:

Answer 3

• Doing work on it
• Adding heat to it

Question 4

The internal energy of a system can decrease by:

Answer 4

• Losing heat to its surroundings

Question 5

Energy can generally be classified into two forms:

Answer 5

• kinetic or potential energy
• The molecules of all substances contain both kinetic and potential energies
• The amount of kinetic and potential energy a substance contains depends on the phases of matter (solid, liquid or gas), this is known as the internal energy

Question 6

The internal energy of an object is intrinsically related to its

Answer 6

• temperature

Question 7

When a container containing gas molecules is heated up, the molecules begin to move around

Answer 7

• faster, increasing their kinetic energy
• If the object is a solid, where the molecules are tightly packed, when heated the molecules begin to vibrate more
• Molecules in liquids and solids have both kinetic and potential energy because they are close together and bound by intermolecular forces

Question 8

ideal gas molecules are assumed to have no

Answer 8

intermolecular forces

• This means there have no potential energy, only kinetic energy

Question 9

• The (change in) internal energy of an ideal gas is equal to:

Answer 9

ΔU=3/2KΔT

• Therefore, the change in internal energy is proportional to the change in temperature:

ΔU ∝ ΔT

• Where:
  
  • ΔU = change in internal energy (J)
  • ΔT = change in temperature (K)

Question 10

As the container is heated up, the gas molecules move faster with higher kinetic energy and therefore higher internal energy

Answer 10

Question 11

EXAM TIP

Answer 11

If an exam question about an ideal gas asks for the total internal energy, remember that this is equal to the total kinetic energy since an ideal gas has zero potential energy

Question 12

Work Done by a Gas

Answer 12

• When a gas expands, it does work on its surroundings by exerting pressure on the walls of the container it’s in
• This is important, for example, in a steam engine where expanding steam pushes a piston to turn the engine

Question 13

The work done when a volume of gas changes at constant pressure is defined as: equation

Answer 13

W = pΔV

• Where:
  
  • W = work done (J)
  • p = external pressure (Pa)
  • V = volume of gas (m³)

Question 14

the gas does work on the piston

Answer 14

• For a gas inside a cylinder enclosed by a moveable piston, the force exerted by the gas pushes the piston outwards

Question 15

Derivation of W = pΔV

Answer 15

• The volume of gas is at constant pressure. This means the force F exerted by the gas on the piston is equal to :

F = p × A

• Where:
  
  • p = pressure of the gas (Pa)
  • A = cross-sectional area of the cylinder (m²)
• The definition of work done is:

W = F × s

• Where:
  
  • F = force (N)
  • s = displacement in the direction of force (m)
• The displacement of the gas d multiplied by the cross-sectional area A is the increase in volume ΔV of the gas:

W = p × A × s

• This gives the equation for the work done when the volume of a gas changes at constant pressure:

W = pΔV

• Where:
  
  • ΔV = increase in the volume of the gas in the piston when expanding (m³)

Question 16

what assumption takes place in the Work done of gas

Answer 16

• This is assuming that the surrounding pressure p does not change as the gas expands
• This will be true if the gas is expanding against the pressure of the atmosphere, which changes very slowly
• When the gas expands (V increases), work is done by the gas
• When the gas is compressed (V decreases), work is done on the gas

Question 17

• When energy is put into a gas by heating it or doing work on it, its internal energy must increase:

Answer 17

The increase in internal energy = Energy supplied by heating + Work done on the system

Question 18

The first law of thermodynamics is therefore defined as

Answer 18

ΔU = q + W

• Where:
  
  • ΔU = increase in internal energy (J)
  • q = energy supplied to the system by heating (J)
  • W = work done on the system (J)

Question 19

The first law of thermodynamics applies to ……..

Answer 19

all situations, not just for gases

• There is an important sign convention used for this equation

Question 20

A positive value for internal energy (+ΔU) means:

Answer 20

• The internal energy ΔU increases
• Heat q is added to the system
• Work W is done on the system (or on a gas)

Question 21

A negative value for internal energy (−ΔU) means:

Answer 21

• The internal energy ΔU decreases
• Heat q is taken away from the system
• Work W is done by the system (or by a gas) on the surroundings

Question 22

Therefore, when the gas expands, work is done by the gas is (positive or negative)

Answer 22

When a gas expands, work done W is negative

(-W)

Question 23

When the gas is compressed, work is done on the gas (positive or negative)

Answer 23

When a gas is compressed, work done W is positive

(+)

Question 24

Positive or negative work done depends on whether the gas is compressed or expanded

Answer 24

Question 25

Graphs of Constant Pressure & Volume

Answer 25

* Graphs of pressure p against volume V can provide information about the work done and internal energy of the gas * The work done is represented by the area under the line * A constant pressure process is represented as a **horizontal line** * If the volume is increasing (expansion), work is done **by** the gas and internal energy increases * If the arrow is reversed and the volume is decreasing (compression), work is done **on** the gas and internal energy decreases * A constant volume process is represented as a **vertical line** * In a process with constant volume, the area under the curve is **zero** * Therefore, no work is done when the volume stays the same

Question 26

***Work is only done when the volume of a gas changes***

Answer 26