The First Law Flashcards
Define internal energy (U)
The total energy a system contains as a result of its physical state
What does the first law state?
Internal energy of a system is constant unless it is changed by work or by heat transfer
U = q + w
What are some characteristics of U?
- U is path independent
- U is a state function
- U is an extensive property
- In microscopic terms, U is equal to the total sum of the energy levels of the atoms or molecules making up the system, weighted by their probabilities of being occupied
What is heat?
The transfer of energy due to a difference in temperature between the system and its surroundings.
If Tsystem < Tsurroundings, q is positive
If Tsurroundings > Tsystem, q is negative
What is work?
A process which could be used directly to move an object a certain distance against an opposing force
Define work of expansion
The work done by the system against the surroundings in moving a piston of area A by distance dz against an opposing force
F(z) = pext(z)A: dw = -F(z) dz = -pextAdz = -Pext(V)dV
What are the characteristics of expansion?
p > pext
Work is negative as the internal energy of the system decreases by carrying work on the surroundings
What are the characteristics of compression?
pext > p
Work is positive as the internal energy of the system increases
What is the determining factor of work done?
external pressure (pext)
What is the work of expansion of a gas against a constant external pressure?
Wext = {pext(V)dv
= -pex deltaV
Work is negative for deltaV postitve
How can the system be changed so the reaction is reversible?
pext must be adjusted to be equal to p at each infinitesimal step in the expression
This keeps the system in equilibrium
What is the ideal gas equation?
pV = nRT
When T is constant,
Wexp = -nRT{1/v dv = -nRTln(Vf/Vin)
How can expansion be carried out irreversibly?
Suddenly lower pext from pa to pb, the expansion occurs against a constant external pressure, pext = pb
The work of expansion is therefore wexp = -pb deltaV
In what system does irreversible expansion occur?
Adiabatic or isothermal
Compare the wexp in irreversible and reversible reactions
wexp (irr) | < |wexp (rev)|
When does a system carry out maximum work?
A system operating between specified initial and final states does the maximum work when the process is carried our reversibly
Is work a state functions?
Work is not a state function as different work was done between the same states in Vin and Vf in reversible and irreversible states
Work is a path function
Is heat a state function?
Heat is not a state function as different work is done between the same states Tinital and Tfinal in the reversible and irreversible states
Heat is a path function
What is a path function?
The values of a path function depend on the path taken between the initial and final states
They are inexact differentials
eg dq and dw
How is U different from q and v?
U only depends on the state of the system and is has a definite value which is independent of path taken (it is a state function)
dU is an exact differential
How can U be written as a function of T and V
dU = (dU/dx)v dT + (dU/dV) dV
The order of differentiation does not affect the result
