# 6.6.1 Gas Laws v Kinetic Theory

### Gas Laws v Kinetic Theory

• There is a scientific distinction between the gas laws and kinetic theory

#### Gas Laws

• The gas laws are empirical in nature which means they are based on observation and evidence
• The gas laws include Boyle’s Law, Charles’s Law, Pressure Law and the ideal gas equation
• These are all based on observations of how a gas responds to changes in its environment, namely volume, pressure and temperature from experiment

#### Kinetic Theory

• Kinetic theory is based on theory (as stated in its name)
• This means it is based on assumptions and derivations from existing theories
• These are then used to explain why the gas laws behave the way they do

### Ideal Gas Internal Energy

• The internal energy of an object is intrinsically related to its temperature
• When a container containing gas molecules is heated up, the molecules begin to move around 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
• However, ideal gas molecules are assumed to have no intermolecular forces
• This means they have no potential energy, only kinetic energy
• This means that the ideal gas internal energy is the kinetic energy of the atoms
• The (change in) internal energy of an ideal gas is equal to: • 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) As the container is heated up, the gas molecules move faster with higher kinetic energy and therefore higher internal energy

#### Worked Example

A student suggests that when an ideal gas is heated from 50 °C to 150 °C, the internal energy of the gas is trebled.

State and explain whether the student’s suggestion is correct.

Step 1: Write down the relationship between internal energy and temperature

• The internal energy of an ideal gas is directly proportional to its temperature

ΔU ∝ ΔT

Step 2: Determine whether the change in temperature (in K) increases by three times

• The temperature change is the thermodynamic temperature ie. Kelvin
• The temperature change in degrees from 50 °C to 150 °C increases by three times
• The temperature change in Kelvin is:

50 °C + 273.15 = 323.15 K

150 °C + 273.15 = 423.15 K • Therefore, the temperature change, in Kelvin, does not increase by three times

Step 3: Write a concluding statement relating the temperature change to the internal energy

• The internal energy is directly proportional to the temperature
• The thermodynamic temperature has not trebled, therefore, neither has the internal energy
• Therefore, the student is incorrect

#### Exam Tip

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

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