Thermodynamics and Gas Laws / Name:
Thermodynamics
Temperature, Kinetic Theory and Thermal Expansion
Heat energy flows from a higher temperature object to a lower temperature object. Temperature represents the average kinetic energy of the molecules in a substance. As the average kinetic energy of the molecules increase, the temperature of the substance will increase. This relationship is known as the kinetic theory of gases.
temperature must be in Kelvin!
kbis Boltzmann’s constant: 1.3806503 × 10-23 m2 kg s-2
Recall:
This “kinetic theory” can be reconfigured to solve for the root-mean-square speed of the molecules:
note: the “m” is the mass of one molecule
As the average kinetic energy of the molecules increase, the molecules will spread out and the object will expand (linear, area & volume).
linear expansion
area expansion
volume expansion
Ideal Gases
When it comes to our study of thermodynamics, we have limited ourselves to ideal gases. A gas is considered “ideal” if:
- The molecules only undergo elastic collisions with the walls of the container and each other.
- The size of the molecules is small compared to the size of the container (i.e. distance between molecules is large).
- The internal energy of the molecules is purely kinetic (i.e. no long range interactions among molecules – no potential energy from molecule to molecule)
- There are a large number of molecules moving in random directions with a variety of speeds.
- The molecules obey Newton’s laws of motion.
To describe a gas fully, we need information on its pressure, volume, temperature and quantity (i.e. number of molecules/moles). This information can be summed up into the Ideal Gas Law:
OR OR
where n is the # of moles and N is the number of molecules. Avogadro’s number tie the two together:
where is Avogadro’s number = 6.02 x 1023 molecules/mole
Thermodynamics
Thermodynamics is the study of the conversion of energy between heat and mechanical. We limited our study to ideal gases. We have already seen above that the average KE of a molecule in a gas can be calculated using the kinetic theory of gases. If this is the average KE for just ONE molecule, then we can determine the total KE of the gas by multiplying this by the total number of molecules! As we assumed in our description of an ideal gas that the internal energy of the gas is purely kinetic, this formula can represent the internal energy of a gas.
R is the Universal Gas Constant: 8.314 J/K
Methods for changing the internal energy of a gas can be summed up by the First Law of Thermodynamics:
Simply stated, the internal energy of a gas can be changed by adding or removing heat energy AND/OR doing work on the gas/having the gas do work. IMPORTANT – the sign conventions are key:
●If heat energy is added to a gas, Q is positive and internal energy will increase
●If heat energy is removed from a gas, Q is negative and internal energy will decrease
●If a gas has work done on it, W is positive and internal energy will increase
●If a gas does work, W is negative and internal energy will decrease
Heat energy can be added to a gas through any method of heat transfer – convection, conduction and radiation.
To do work on a gas, or have a gas do work, its volume MUST change. Recall the area under a Pressure vs. Volume diagram is work. To determine if work is done by or on the gas, look at what happens to volume:
●If the volume of the gas increases, the gas did work
●If the volume of the gas decreases, work was done on the gas
We looked at four different thermodynamic processes and their associated PV diagrams. You should familiarize yourself with what these diagrams look like.
1.Isothermal Process – constant temperature process
●Since temperature doesn’t change and internal energy is a function of temperature, we can conclude that ΔU=0.
●Also, since temperature is a constant, we can conclude based on the Ideal Gas Law that the product of PV will be a constant as well.
●If the system does work, then heat must be added to the system to compensate for the energy lost doing work in order to maintain a zero change in internal energy.
●If work is done on the system then heat must be removed to the system to compensate for the energy gained by the work in order to maintain a zero change in internal energy.
- Adiabatic Process – no heat transfer in or out of the system
●Q = 0
●ΔU = W
●If the system does work then ΔU decreases and therefore the temperature of the gas decreases as well.
●If work is done on the system then ΔU increases and therefore the temperature of the gas increases as well.
- Isobaric Process – constant pressure process
●Since the PV curve of an isobaric process is a horizontal line, it is very easy to calculate the work by calculating the area under the PV graph. W = PΔV
●No conclusions can be drawn about Q as it may be added or removed – need to handle on a case by case basis.
- Isometric Process – constant volume process
●The PV graph for an isochoric process is a vertical line. Thus, NO work can be associated with an isochoric process as there is NO area under the PV graph.
●The change in internal energy depends ONLY on the heat added or removed from the gas. As heat is added, ΔU increases and temperature increases. As heat is removed, ΔU decreases and temperature decreases.
General info for any cyclical process:
●If a gas starts and ends at the same position on a PV diagram its change in internal energy is 0 as its starting and ending temperature are the same.
●If a cyclical process is clockwise, the gas did work and therefore the total work done can be considered negative. You can quickly calculate this work by determine the area enclosed by the PV diagram. This process would represent a heat engine as thermal energy was transferred into mechanical energy.
●If a cyclical process is counter-clockwise, work was done on the gas and therefore the total work done can be considered positive. You can quickly calculate this work by determine the area enclosed by the PV diagram. This process would represent a refrigerator.
The Second Law of Thermodynamics states that heat flows naturally form high temps to low temps and never in reverse. As the heat is flowing, some can be converted into mechanical energy to do work. From the conservation of energy we can conclude:
QH = W + QL
Heat energy can NEVER be completely transferred into work. As a result, we often measure the efficiency of an engine to indicate just how much heat energy is converted into work.
The most efficient energy is considered the Carnot Engine. It is made up of two adiabatic and two isothermal processes and is considered a reversible process. As a result, the Carnot Efficiency is often thought of as the Ideal or Maximum Efficiency for a given engine operating between two different temperatures. The Carnot Efficiency can be calculated using:
Practice Problems
2010
2009b
2008b
2007b
2006
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