1. Gas particles are in constant, random motion
2. Collisions are elastic
3. Negligible forces between gas particles
4. Negligible volume of particles
5. Temperature is average kinetic energy of all particles in substance. Plateaus on $a$ and $b$ due to energy being used to break intermolecular bonds instead of increasing kinetic energy.

Fun note: To boil, gas particles escape liquid. Increasing pressure increases boiling point. Thats how pressure cookers work! Vapour pressure > External pressure = Boiling