Chemistry 231Chapter 3 – Enthalpy and Internal Energy:

The Importance of State Functions

Let’s examine the pressure of any system as a function of T and V

The Properties of the Pressure, P

V T

P PdP dT dV

T V

For a fluid system or a solid• Isothermal Compressibility

The Isothermal Compressibility

TT P

VV

1

For solids and fluid systems• The coefficient of thermal expansion

Coefficient of Thermal Expansion

PTV

V

1

Assume that we will write pressure as a function of T and V

The Final Expression

1

T T

dP dT dVV

In general, we write U as a function of T and V

The Properties of U

V

T

UdU C dT dV

V

Examine the second partial derivative

Isothermal Changes in U

dVVU

dUT

The Joule Experiment

AT1, Vm,1, P1

B

Stirrer

Valve

Thermal insulationFFOO

CO

CO

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The partial derivative

The Joule Coefficient

is known as the Joule coefficient, J. UV

T

The change in the internal energy under isothermal conditions is related to the Joule Coefficient

Internal Energy and the Joule Coefficient

VUT TU

VT

VU

JVT

CVU

For an ideal gas

Relating CP and CV

nRCC VP

In general

TVP

TVCC

2

In general, we write H as a function of T and P

The Properties of H

p

T

HdH C dT dP

P

Define the constant pressure heat capacity, CP

The Constant Pressure Heat Capacity

PPP T

HdTdq

C

Examine the second partial derivative

Isothermal Changes in H

dPPH

dHT

0

The Joule-Thomson Experiment

Porous Plug

Thermal insulation

T1, P1, Vm,1T2, P2, Vm,2

FFOO

CO

CO

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FFOO

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CO

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The partial derivative

The Joule-Thomson Coefficient

is known as the Joule-Thomson coefficient, JT.

HPT

The change in the enthalpy under constant pressure conditions is related to the Joule-Thomson Coefficient

Relating H to the Joule-Thompson Coefficient

PHT TH

PT

PH

JTPT

CPH