- Changes in the state of a system are produced by interactions with the environment through heat and work.
- During these interactions, equilibrium (a static or quasi-static process) is necessary for the equations that relate system properties to one-another to be valid.
- Heat and work are transfers of energy across a system boundary
Work done by system
or in terms of the specific volume, v:
where m is the mass of the system.
If system volume expands against a force, work is done by the system.
If system volume contracts under a force, work is done on the system.
Why pexternal instead of psystem?Consider pexternal = 0 (vacuum). No work is done by the system even though psystem changes and the system volume changes.
Use of pext instead of psys is often inconvenient because it is usually the state of the system that we are interested in.
However, for quasi-static processes psys Å pext..
Consider pext = psys ± dp
is the work done by the system in a quasi-static process.
Can only relate work to system pressure for quasi-static processes.
Take a free expansion (pext = 0) for example: psys is not related to pext ( and thus the work) at all -- the system is not in equilibrium.
Work depends on path
Work is not a function of the state of a system
Must specify path if we need to determine work
Along Path a: W = 2p0(2V0 - V0) = 2p0V0
Along Path b: W = p0(2V0 - V0) = p0V0
Example: Work during quasi-static, isothermal expansion of a thermally perfect gas from p1, V1 to p2, V2 .
First, is path specified? Yes -- isothermal.
Equation of state for thermally perfect gas
pV = nRT n = number of moles
R = Universal gas constant
V = total system volume
also for T = constant, p1V1 = p2V2 , so the work done by the system is
or in terms of the specific volume and the system mass
Can have one, the other, or both. It depends on what crosses the system boundary. For example consider a resistor that is heating a volume of water.
If the water is the system, then the state of the system will be changed by heat transferred from the resistor.
If the system is the water + the resistor, then the state of the system will be changed by (electrical) work.
Homework 2 (PDF)