6.6.1 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

• 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

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