Physical Chemistry I(TKK-2246)

13/14 Semester 2

Instructor: Rama OktavianEmail: rama.oktavian86@gmail.comOffice Hr.: M.13-15, Tu. 13-15, W. 13-15, Th. 13-15, F. 09-11

Outlines

1. Expansion work

2. Multistage expansion

3. Work of expansion

4. Maximum and minimum work

Review1. 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.

Review1. 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 walk-up 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 thermodynamicsMathematical 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 currentthrough 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 theatmosphere

- The term ‘expansion work’ also includes work associated with negativechanges 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

Fdzdw

Expansion work

General expression of expansion work

Fdzdw ApF ext

Adzpdw ext

AdzdV

dVpdw ext the work arising from a change in volume

Expansion work

General expression of expansion work

dVpdw extIntegrating equation from initial to final volume

dVpwf

i

V

Vext

Expansion workReversible expansion

In a reversible process the system is at equilibrium at every stage of the process

Reversibility during pressure changes ensures that

ppext

the pressure on the inside of the container is always equal to the pressure exerted on the outside of the container

Expansion workReversible expansion

When we set pex = p

ppext

the pressure on the inside of the container is always equal to the pressure exerted on the outside of the container

pdVdVpdw ext The total work of reversible expansion is therefore

f

i

V

Vrev pdVw

Expansion workIsothermal reversible expansion

Consider the isothermal, reversible expansion of an ideal gas

nRTpV

the work of reversible isothermal expansion of a perfect gas from Vi to Vf at a temperature T is

i

fV

Vrev V

VnRT

VdVnRTw

f

i

ln

Expansion workIsothermal reversible expansion

Expansion workIsothermal reversible expansion

Multistage expansion workMultistage irreversible isothermal expansion and compression

n

nnWW

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 area50.0 cm2. As a result of the reaction, a piston is pushed out through 15 cmagainst an external pressure of 121 kPa. Calculate the work done by thesystem

ExerciseIsothermal compression

A sample consisting of 2.00 mol He is expanded isothermally at 22°Cfrom 22.8 dm3 to 31.7 dm3 (a) reversibly, (b) against a constant externalpressure equal to the final pressure of the gas. For the two processes calculate w

ExerciseIsothermal 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