Physical Chemistry , 1st ed.

Example 2.7

A 1.00-L sample of gas at 1.00 atm pressure and 298 K expands isothermally

and reversibly to 10.0 L. It is then heated to 500 K, compressed to 1.00 L, and

then cooled to 25°C. What is Ufor the overall process?

Solution

U0 for the overall process. Remember that a state function is a variable

whose value depends on the instantaneous conditions of the system. Since

the initial and final conditions of the system are the same, the system has the

same absolute value of internal energy (whatever it might be), so that the

overall change in the internal energy is zero.

2.5 Enthalpy

Although the internal energy represents the total energy of a system, and the

first law of thermodynamics is based on the concept of internal energy, it is not

always the best variable to work with. Equation 2.15 shows that the change in

the internal energy is exactly equal to q—if the volume of the system remains

constant for a particular process. However, the experimental condition of con-

stant volume can be difficult to guarantee for many processes. Constant pres-

sure, considering that many experiments occur exposed to the atmosphere, is

often an easier experimental parameter.

Enthalpyis given the symbol H. The fundamental definition of enthalpy is

HU+ pV (2.16)

The pressure in equation 2.16 is the pressure of the system,pint. Enthalpy is

also a state function. Like internal energy, the absolute value of the enthalpy is

unknowable, but we can determine changesin the enthalpy,dH:

dHdU+ d(pV) (2.17)

The integrated form of this equation is

HU+ (pV) (2.18)

Using the chain rule of calculus, we can rewrite equation 2.17 as

dHdU+ p dV+ V dp

For a constant pressure process (which is more common in laboratory exper-

iments), the Vdpterm is zero because dpis zero. Using the original definition

ofdU, the equation becomes

dHdq+ dw+ p dV

dHdqp dV+ p dV

dHdq (2.19)

In terms of overall changes to a system, equation 2.19 can be integrated to get

Hq

Since the process occurs at constant pressure, the last equation is written like

equation 2.15 as

Hqp (2.20)

36 CHAPTER 2 The First Law of Thermodynamics