Thermodynamic Systems (DP IB Physics)

Change in Internal Energy

• The change in the internal energy of an object is intrinsically related to a change in its temperature

• When a container containing gas molecules is heated up, the molecules begin to move around faster, increasing their kinetic energy

  • In a solid, where the molecules are tightly packed, molecules begin to vibrate more as they are heated

  • Molecules in liquids and solids have both kinetic and potential energy because they are close together and bound by intermolecular forces

• However, the molecules in an ideal gas are assumed to have no intermolecular forces

  • This means they do not possess potential energy, only kinetic energy

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

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

• Where

  • = change in internal energy (J)

  • = Boltzmann constant

  • = change in temperature (K)

  • = number of particles

• Another form of this equation related to the translational kinetic energy of the particles is

• Where:

  • = number of moles of gas (mol)

  • = molar gas constant

Work Done by a Gas

• When a gas expands, it does work on its surroundings by exerting pressure on the walls of the container it's in

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

  • As a result, work is done on the piston by the gas

• Alternatively, if an external force is applied to the piston, the gas will be compressed

  • In this case, work is done on the gas by the piston

The expansion of the gas does work on the piston by exerting a force over a distance, s

• Assuming the volume of gas is kept at constant pressure, this means the force F exerted by the gas on the piston is equal to:

• Where A = cross-sectional area of the cylinder (m²)

• The definition of work done is:

• Where s = displacement in the direction of force (m)

• The displacement s of the gas multiplied by the cross-sectional area A is equal to the increase in volume ΔV of the gas:

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

• Where:

  • W = work done (J)

  • p = pressure of the gas (Pa)

  • ΔV = change in the volume of the gas (m³)

• This equation assumes that the surrounding pressure does not change as the gas expands

  • This is true if the gas is expanding against the pressure of the atmosphere, which changes very slowly

p-V diagrams

• Pressure-volume (p-V) diagrams are often used to represent changes in the state of a gas in thermodynamic processes

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

• When a gas expands (at constant pressure) work done is positive

  • Volume increases +ΔV

  • Work is done by the gas +W

• When a gas is compressed (at constant pressure) work done W is negative

  • Volume decreases −ΔV

  • Work is done on the gas −W

• When both the volume and pressure of gas changes

  The work done can be determined from the area under a p-V diagram