Thermal Equilibrium

Thermal equilibrium is when there is no longer a flow of energy between two objects. If a piece of ice is placed in a glass of water that is at room temperature, thermal energy will flow from the water to the ice. Eventually the ice and the water will be at the same temperature. At this point, thermal equilibrium has been established. When two substances are mixed or in contact, heat lost by one substance is equal to the heat gained by the other substance. 

The zeroth law of thermodynamics states that if two thermodynamic systems are each in thermal equilibrium with a third, then they are in thermal equilibrium with each other. 

The first law of thermodynamics states that energy cannot be created or destroyed but only transformed into other forms of energy. The total energy of a system is always a constant.

Heating and Cooling Curves

When a substance is heated, the temperature of the substance is directly proportional to the thermal energy that has been put into the substance by some external source. This is assuming that the substance does not change phase, has constant mass and the rate of thermal energy input is constant.

A key point above is that the substance does not change phase. In the diagram below a graph of time vs temperature demonstrates the changes between the different states of water. Note that the graph is flat during a phase change. This is because the thermal energy during a phase change goes into breaking the intermolecular bonds between particles rather than increasing the kinetic energy of the particles.

 

 

 

Elastic and Inelastic Collisions

An elastic collision occurs when kinetic energy is conserved, that is the initial kinetic energy = the final kinetic energy of the system. 

  • In elastic collisions the kinetic energy of the system is conserved.
  • In inelastic collisions the kinetic energy of the system is not conserved.
  • In all collisions the total momentum of the system is conserved.

When an inelastic collision occurs there will be a loss of kinetic energy. The kinetic energy lost is transformed into other forms of energy (heat, light, sound). The objects in the system may also become deformed (bent, crushed, broken), or the objects may collide and stick together (train engine coupling with carriage).

Example 1:

A 250g toy car travelling at 5\cfrac { m }{ s } east, collides with an identical toy car travelling in the same direction at 2.5\cfrac { m }{ s } . After the collision the first car continues in the same direction at 1.5\cfrac { m }{ s } . The second car continues in the same direction after the collision at 4\cfrac { m }{ s } . Is this collision elastic or inelastic?

{ m }_{ 1 } = 250g

{ u }_{ 1 } = 5\cfrac { m }{ s } to the east (note: east as positive)

{ v }_{ 1 } = 1.5\cfrac { m }{ s } east 

{ m }_{ 2 } = 250g

{ u }_{ 2 } = 2.5\cfrac { m }{ s } east

{ v }_{ 2 } = 4\cfrac { m }{ s } east

We need to compare the initial kinetic energy to the final kinetic energy of the system:

KE_{ i }={ KE }_{ 1 }+{ KE }_{ 2 }

KE_{ i }=\cfrac { 1 }{ 2 } mu^{ 2 }(car1)+\cfrac { 1 }{ 2 } mu^{ 2 }(car2)

KE_{ i }=\cfrac { 1 }{ 2 } \times 0.25\times { 5 }^{ 2 }+\cfrac { 1 }{ 2 } \times 0.25\times { 2.5 }^{ 2 }

KE_{ i }=3.125+0.781

KE_{ i }=3.91J

KE_{ f }={ KE }_{ 1 }+{ KE }_{ 2 }

KE_{ f }=\cfrac { 1 }{ 2 } mv^{ 2 }(car1)+\cfrac { 1 }{ 2 } mv^{ 2 }(car2)

KE_{ f }=\cfrac { 1 }{ 2 } \times 0.25\times { 1.5 }^{ 2 }+\cfrac { 1 }{ 2 } \times 0.25\times { 4 }^{ 2 }

KE_{ f }=0.281+2

KE_{ f }=2.28J

Therefore; KE_{ i } does not = KE_{ f } and the collision was inelastic.