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14/15 Semester 2
Physical Chemistry I
(TKK-2246)
Instructor: Rama Oktavian
Email: [email protected]
Office Hr.: M – F.13-15
Outlines
1. Expansion work
2. Multistage expansion
3. Work of expansion
4. Maximum and minimum work
Review
1. Suggest a system, boundary, and surroundings for 10 moles of propane gas
in a rigid metal cylinder
2. Suggest a system, boundary, and surroundings for 500 mL of water in an
open beaker.
Review
1. Describe three commonplace examples of how work is done on or by a
system
2. A plumber of mass 65 kg carries a toolbox of mass 15 kg to a fifth floor walkup apartment 15 m above ground level. Calculate the work required for this
process
3. Describe the internal energy change and work performed when a spring is
compressed or expanded.
1st law of thermodynamics
Mathematical statement for The 1st Law of Thermodyamics
ΔU = q + w
in which w > 0 or q > 0 if energy is transferred to the system as work or heat
and w < 0 or q < 0 if energy is lost from the system as work or heat
Heat, work, and energy
Work (W) - any quantity that flows across the boundary of a system during a
change in its state
Ex:
- gas that pushes out a piston and raises a weight
- A chemical reaction that drives an electric current
through a resistance also does work
Expansion work
the work arising from a change in volume
Ex:
- the work done by a gas as it expands and drives
back the
atmosphere
- The term ‘expansion work’ also includes work
associated with negative
changes of volume, that is, compression
Expansion work
General expression of expansion work
the work required to move an object a distance dz
against an opposing force of magnitude F is
dw   Fdz
Expansion work
General expression of expansion work
dw   Fdz
F  pext A
dw   pext Adz
dV  Adz
dw   pext dV the work arising from a change in volume
Expansion work
General expression of expansion work
dw   pext dV
Integrating equation from initial to final volume
Vf
w    pext dV
Vi
Expansion work
Reversible expansion
In a reversible process the system is at equilibrium at every stage of the
process
Reversibility during pressure changes ensures that
pext  p
the pressure on the inside of the container is always equal to the pressure
exerted on the outside of the container
Expansion work
Reversible expansion
When we set pex = p
pext  p
the pressure on the inside of the container is always equal to the pressure
exerted on the outside of the container
dw   pext dV   pdV
The total work of reversible expansion is therefore
Vf
wrev     pdV
Vi
Expansion work
Isothermal reversible expansion
Consider the isothermal, reversible expansion of an ideal gas
pV  nRT
the work of reversible isothermal expansion of a perfect gas from Vi to Vf at a
temperature T is
Vf
Vf
dV
wrev   nRT 
 nRT ln
V
Vi
Vi
Expansion work
Isothermal reversible expansion
Expansion work
Isothermal reversible expansion
Multistage expansion work
Multistage irreversible isothermal expansion and compression
n
W   Wn
n 1
where n is number of stage
Maximum and minimum work
Reversible processes actually do not occur
in nature
They are simply idealization of actual
Processes
Easy to analyze
Serve as idealized model
Maximum and minimum work
when Reversible processes are
approximated instead of the Actual ones
Work-producing devices such as car
engine and gas or steam turbine deliver
the maximum work, and
Work-consuming devices such as
compressors, fan, and pumps
Consume the minimum work.
Exercise
A chemical reaction takes place in a container of cross-sectional area
50.0 cm2. As a result of the reaction, a piston is pushed out through 15 cm
against an external pressure of 121 kPa. Calculate the work done by the
system
Exercise
Isothermal compression
A sample consisting of 2.00 mol He is expanded isothermally at 22°C
from 22.8 dm3 to 31.7 dm3 (a) reversibly, (b) against a constant external
pressure equal to the final pressure of the gas. For the two processes calculate w
Exercise
Isothermal compression, maximum and minimum work
Three moles of an ideal gas are compressed isothermally from 60 L to 20 L using
a constant pressure of 5 atm. Calculate W.
If that gas is compressed reversibly, calculate W