Energy and Gases

Energy Definitions

Energy: having the ability to do work (move matter)

Work: a push or pull over some distance (force x distance)

Force: a push or a pull

Potential Energy:   the energy a body possesses by virtue of its position, composition, and or condition
                                stored energy or energy of position
                                P.E. = mass x gravity x height
                                examples: water behind a dam, stretched/compressed spring, explosives

Kinetic Energy:   the energy of motion (conserved in every elastic collision)
                                K.E. = 1/2 mass x velocity squared
                                heat energy flows from hot objects to cooler ones through transfer of K.E. when particles collide

Momentum: mass time velocity (momentum is conserved in every collision where there is no friction)

Linear momentum of a moving body is a measure of its tendency to continue in motion at a constant velocity. The conservation of linear momentum states that in the absence of forces from outside the system the total momentum of colliding particles cannot change but the distribution of the total momentum may change. Momentum is redistributed in a collision.

Intermolecular Forces:

	potential energy forces that hold molecules together and in correct position in solids
	potential energy forces that hold molecules together in liquids
	the kinetic energy of the molecules in solids and liquids cannot overcome intermolecular forces holding the molecules together (so they do not fly apart)
	gas molecules have enough kinetic energy to break free from intermolecular forces or to keep such forces from forming

Kinetic – Molecular Theory of Gases

	gases are made up of molecules that are in continuous motion
	an increase in the temperature increases the speed of the molecules, thus increasing the kinetic energy of the substance
	All gases are compressible
	Gases display diffusion (random movement of molecules from one area to another with a net change in concentration – rate varies with temperature and molecular mass)
	Gases can be liquefied (called liquefaction)

Closed System Criteria

In using the above information we look at pressure, temperature, and volume in a closed system.

In a closed system nothing escapes or is allowed in (unless we choose to allow it)
all molecules are in motion (have K.E.)
molecules exert a uniform pressure on all surface areas of the walls of the container
Pressure = force/area (see examples given in class)
Atmospheric pressure is the cumulative effect of the force generated by the weight of the atmosphere. Given values that must be used in problems include: 14.7 lb/in², 101.3 kPa, 1 atmosphere, 760 mm of Hg, 1 033.6 g/cm²
Molecules exert pressure on other molecules inside container as they collide, push, and bounce off other molecules
The pressure a gas exerts on the walls of its container is the sum of the forces acting on the walls (equals the frequency of collisions with the walls of the container plus the force of each molecule as it pushes against the wall) due to the random collision of limitless numbers of these moving molecules.

Collisions that occur between molecules are perfectly elastic, the particles bounce off each other and exchange energy, but there is no loss of energy
* elastic atomic collisions: atoms (molecules) bounce back as far/fast as it would have had it not collided (no change in the total kinetic energy of the two particles before and after the collision)
* inelastic collisions: the normal order in which the objects lose energy and slow down

Momentum is conserved in every collision where there is no friction, energy is conserved only in elastic collisions.

Gas Laws

J.L. Gay-Lussac’s Law If the volume remains constant, the pressure is directly proportional to the absolute temperature:

P ~ T P₁/ T₁ = P₂ / T₂

Boyle’s Law If the temperature remains constant, the volume of a gas varies inversely with the pressure:

V ~ 1/P P₁ V₁ = P₂ V₂

Charles’ Law If the pressure is kept constant, the volume of a gas is directly proportional to its absolute temperature:

V ~ T V₁/ T₁ = V₂ / T₂

For each degree increase in temperature, the volume increases 1/273 of its original volume

Combined gas law:

P₁V₁ / T₁ = P₂ V₂ / T₂

5. Ideal Gas Law:

PV = nRT

Overall conclusions:

	The temperature of a gas increases when it is compressed because the average energy of its molecules increases. The molecules rebound from the inward moving piston, traveling faster than before hitting the piston.
	Molecules rebounding from fixed walls have unchanged speeds.
	The temperature of a gas decreases when its volume is expanded because the average energy of its molecules decreases. The molecules rebounding from outward moving piston move slower than before.

Gas Law Problems:

1) An insulated system is known to have a temperature of 100.0° C at a pressure of 4.00 atm. If the absolute temperature is cut in half, what will be the new:

___________ atm, __________kPa, ______________° C, _______________ K

2) The volume is given as 27.0 L. If the pressure goes from 3.00 atm. to 9.00 atm., what is the new:

___________L, _____________ kPa

3) The volume is given as 5.00 L. If the absolute temperature goes from 273 to 819 K, what is the the new __________L (if new temperature was 800. K, what is the new volume in liters?)

4) The temperature is given as 25.0° C. If the volume is decreased from 100. mL to 10.0 mL, what is the new: ____________K, ____________° C