Exam 2 Flashcards
(69 cards)
4 postulates of Kinetic theory of gases
- Gas consists of a large number of identical molecules separated by distances that are great compared to their size
- Gas molecules are constantly moving in random directions with a distribution of speeds
- Molecules can collide with each other (bounce off each other with no loss of kinetic energy) but exert no forces on one another between collisions
- The collisions of molecules with the walls of the container are also elastic (no loss of kinetic energy)
Kinetic theory of gases
a model for molecular motion that predicts the properties of gases, particularly the relationship between temperature and the distribution of molecular speeds
Maxwell-Boltzmann plot (with constant molecule mass but varying temperature)
-Low temperature will have higher peak, more condensed shape, and lower average speed (closer to 0)
-Higher temperature will have lower peak, more spread out shape, and higher average speed (farther from 0)
Maxwell-Boltzmann plot (with constant temperature but varying molecule mass)
-Higher molecular mass will have higher peak, more condensed shape, and lower average speed (closer to 0)
-Lower molecular mass will have lower peak, more spread out shape, and higher average speed (farther from 0)
<V> (mean speed
</V>
-<V> = √8kBT/πm or √8RT/πm
-Will always be greater than most probable speed, as area under the curve to the right is somewhat larger than the area under the curve to the left
-<v> = (1.128)(Vmp)</v></V>
mean square speed
-<v^2> = √3kBT/m
-Directly related to KE (½mv^2)
Vmp (most probable speed)
-Vmp = √2kBT/m or √2RT/m
-Found at the peak of the graph
-will always be less than <v></v>
Area under Maxwell-Boltzmann plot
-Total area always equals 1 (100% of molecules)
-To find fraction of molecules under graph with given range of speeds, find number of molecules at max of range and min of range and take max - min
-Act like the max of graph=1 and add max y to min y value then times by percentage of graph x values take up
Total kinetic energy (monatomic gas)
-KE(total translational) = 3/2nRT
-KE total also equals = N<KE>
-Total kinetic energy increases linearly with temperature, depends on both temperature and number of molecules in sample</KE>
Average translational kinetic energy (for a single gas molecule)
-<KE> = 3/2 kT
-Average kinetic energy is the same for all molecules at a given temperature (depends only on temperature)
-increases linearly with temperature</KE>
Thermodynamics
-concerned with macroscopic properties of systems and changes in these properties during processes
-Study of the interconversion, transfer, and dispersal of energy among its various forms
Thermodynamic system
-a real or imagined portion of the universe that is confined by boundaries or mathematical constraints
Open system
both matter and energy may be freely exchanged with the surroundings
Closed system
does not gain or lose matter during a process because it is surrounded by impermeable walls
Isolated system
system which is surrounded by walls that prevent it from exchanging energy or matter with its surroundings
State function
-a property of a system that is uniquely determined by the present state of a system and not at all by its history
-Volume temperature, pressure, and internal energy (U) are examples of state functions
-the value of ΔU (or ΔV or ΔT) depends only on the initial and final states of the system, not the path by which the process got the system from initial to final
Path function
-a property of a system that is uniquely determined by the specific path taken to transition from initial to final states, rather than just the state itself
-Work and heat are path functions
-Path-dependent, values vary depending on how the process occurs not just the initial and final states
First law of thermodynamics
-in any process, energy can be changed from one form to another (eg potential to kinetic) and energy can be transferred from one object to another (as heat or work), but energy is never created or destroyed
-Law of conservation of Energy
-If energy change is caused by mechanical contact of system with its surroundings, work is done
-If energy change is caused by thermal contact, heat is transferred
Internal energy (U)
-the sum of internal kinetic energy and potential energies of the particles composing a system
-Any mechanical or electrical work done on a system can change its internal energy (unless heat is transferred out of system to compensate)
-For idea monatomic gases, U = KE (3/2nRT)
-ΔU = 3/2nRΔT
-ΔU = q + w
Work (w)
-the product of the external force F acting on a body and its displacement d
-W > 0, work is done on system by the surroundings
-W < 0, work is done by system onto surroundings
Pressure-Volume work
-results when system is compressed or expanded under influence of outside pressure
-w = -PextΔV
-For expansion, ΔV > 0 , and work is being done by system
-For compression, ΔV < 0, and work is being done by surroundings
-Can be reversible or irreversible
Isothermal reversible gas expansion/compression
-internal pressure is nearly equal to the external pressure and expansion/compression is slow
-w(rev exp) = -nRTln(V2/V1)
-w(rev comp) = -nRTln(V1/V2)
-Most efficient, maximum work is done
Irreversible process
-a process that does not proceed through a series of equilibrium states and cannot be reversed by an infinitesimal change in an external force
-Rapid and uncontrolled
-Cannot be represented by path
-Pext is constant and often lower/higher than internal (depending on if expansion/compression)
Reversible process
-a process that proceeds through a series of equilibrium states, and can be reversed by an infinitesimal change in external force
-Pint and Pext are nearly equal
-maximum possible work is done by gas
-Follows well-defined path
