Physical Chemistry I (TKK-2246)

Physical Chemistry I(TKK-2246)

13/14 Semester 2

Instructor: Rama OktavianEmail: [email protected] Hr.: M.13-15, Tu. 13-15, W. 13-15, Th. 13-15, F. 09-11

Outlines

1. Change in energy

2. Change in state at constant volume

3. Change in state at constant pressure

4. Adiabatic change state(Process calculation in ideal gas)

Change in energyEnergy is an extensive state property of the system

Energy per mole is an intensive state property of the system

Energy is conserved in all transformations

First law thermodynamic

dU = dQ + dW

dU of the system depends only on the initial and final states

Q and W depends on path

Change in energyFirst law thermodynamic

dU = dQ + dW

dU of the system depends only on the initial and final states. Define U = U(T,V)

dVVUdT

TUdU

TV

Substituting dU from the first law thermodynamic

dVVUdT

TUdWdQ

TV

Change in energyFirst law thermodynamic

dVVUdT

TUdWdQ

TV

pdVdW

dVVUdT

TUpdVdQ

TV

Change in energyFirst law thermodynamic

dVVUdT

TUdWdQ

TV

pdVdW

dVVUdT

TUpdVdQ

TV

Change in energyFirst law thermodynamic

dVVUdT

TUpdVdQ

TV

)()( nVpddQnUd

This is the general first-law equation for a mechanically reversible, closed-

system process

Change in energyExample of energy change – state and path function

Change in state at constant volumeFirst law thermodynamic

dVVUdT

TUpdVdQ

TV

)()( nVpddQnUd

Change state at constant volume

0dV dTTUdQ

V

Change in state at constant volumeNew properties – heat capacity

Heat capacity at constant volume

dTTUdQ

V

VTU

dTdQ

VV T

UC

Change in state at constant volumeHeat calculation at constant volume

If Cv constant

VV T

UC

dTCdU V

2

1

2

1

T

TV

U

U

dTCdU

2

1

2

1

T

TV

U

U

dTCdU

Change in state at constant volumeHeat calculation at constant volume

)()( nVpddQnUd

dUdQ

2

1

U

U

dUQ12 UUQ

2

1

2

1

T

TV

U

U

dTCdU

Valid for constant volume process

2

1

T

TVdTCQ Heat calculation at constant volume process

Change in state at constant pressureIn laboratory practice most changes in state are carried out under a constant atmospheric pressure

Change in state at constant pressureRecall first law thermodynamics mathematical formulation

)()( nVpddQnUd Integrating this equation at constant pressure, we obtain

Change in state at constant pressure

Rearranging this equation

Change in state at constant pressureIntroducing new extensive state property of system

Enthalpy

Valid for constant-pressure process

Change in state at constant pressureHeat calculation at constant pressure process

constant pressure process

Change in state at constant pressureHeat calculation at constant pressure process

Heat capacity at constant pressure process

Valid for constant pressure process

If Cp is constant

Implied property relation for ideal gas Relation between Cv and Cp

VV T

UC

Adiabatic changeAdiabatic – no heat flow

the first law statement is

dWdU

pdVdU

Adiabatic changeAdiabatic change state in ideal gas

pdVdTCv For ideal gas nRTpV

Adiabatic change

Integrating this equation from initial state (T1, V1) into final state (T2, V2), we have

If Cv is independent to temperature (T)

Adiabatic change

For ideal gas we have relationship

Adiabatic changePVT relationship for adiabatic change state in gas ideal

Adiabatic changeAdiabatic change PV-graph

Learning checkCheck and Re-do example 7.3 from Castellan

An ideal gas, Cv = 5/2 R, is expanded adiabatically against a constant pressure of 1

atm until it doubles in volume. If the initial temperature is 25 °C, and the initial

pressure is 5 atm, calculate T2 ; then calculate Q, W, ΔU, and ΔH per mole of

gas for the transformation.

Assignment

Open your textbook (Castellan) and do these following problem:

Problem 7.1, 7.4, 7.10, 7.15, 7.17

The constant-pressure heat capacity of a sample of a perfect gas was found to vary

with temperature according to the expression Cp /(J K−1) = 20.17 + 0.4001(T/K).

Calculate q, w, ΔU, and ΔH when the temperature is raised from 0°C to 100°C (a) at

constant pressure, (b) at constant volume.

Process in ideal gas

Isothermal Process (constant temperature) for closed system process

Governing equation

Process in ideal gas

Isobaric Process (constant pressure) for closed system process

dTCU V

HQ

Process in ideal gas

Isochoric Process (constant volume) for closed system process

UQ

Process in ideal gas

Example