MOaD 6 Flashcards
(29 cards)
What conditions can a gas expand?
isothermal
adiabatic
adiabatic gas expansion
system is thermally insulated / temperature is not constant
isothermal gas expansion
heat can be exchange with the environment. temperature is constant
adiabatic gas expansion cannot
rely on getting help from the environment from heat/energy
adiabatic and isothermal have different…
variation of p and v
how can isothermal conditions be achieved?
in a water bath
boyles law
p1v1 = p2v2
differentiation of work done in a gas?
dw = -p dV
Intergration of work done in a gas?
-p dV
What is an instaneous expansion?
irreversible
What happens in instaneous expansion?
Forcing back the external atmosphere which is at a constant pressure.
What is the formula for instaneous expansion relating to work?
w = -pextΔV
free expansion
‘free expansion’ , there is zero external pressure, pext = 0 so w = 0.
infinitely slow expansion
Now let’s do the same expansion, except do it infinitely slowly, such that at any
instant heat can flow to/from the gas keeping the temperature constant. This process would be reversible, since none of the energy we want to spend on work is wasted as heat.
work done in a reversible expansion formula
w = -nRT ln (Vf / Vi)
perfect gas in reversible expansion internal energy formula
ΔU = q + w = 0
What is the work done, and the heat gained, when 1 mol of a perfect gas is expanded
isothermally and reversibly to twice its original volume at 298 K?
Vf = 2V1
, so
w = - 1 × 8.314 × 298 × ln (2/1)
w = -1.72 kJ
q = -w = +1.72 kJ
ΔU = q + w = 0
work pressure and volume formula
w = -pf ΔV
in irreversible reactions with -pv V what is the expansion
By breaking the process down into two smaller steps
we got more work out of the gas.
using the Reversible Work formula is…..
Maximum Work
Reversible Work formula
w = -RT ln(Vf / Vi )
why does reversible work have a greater work than irreversible?
the expansion was done so quickly that the surroundings didn’t have chance to equilibrate with the system, and so not all the available heat was transferred.
so less energy was available to do work.
what does the 1st law of energy say for the internal energy of a gas that is expanding reversible
Energy must be conserved, so using the 1st Law and realising that ΔU=0, then q = -w.
what does the 1st Law suggest the surroundings do?
- So the surroundings had to supply heat to the system, which provided the extra energy
for work, and this was the maximum heat that could be supplied.
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