BioPHYSICAL chemistry

form. The internal energy, U, is a measure of the total

capacity of the system to release heat or perform work.

When work is done on a system the internal energy will

increase; likewise when heat is applied (Figure 2.6).In most

cases, the absolute value of the internal energy cannot

be determined, but the change in energy can be measured.

Therefore, we can define the change in the internal energy,

ΔU, as the sum of the energy transferred into the system

as work, w, and the energy transferred into the system as

heat, q:

ΔU=q+w (2.13)

When pressure is held constant, work contribution is given by the volume

change. The change in internal energy can then be related to the volume

change:

ΔU=q+w=q−PΔV (2.14)

Consider how work, internal energy, and enthalpy are related for an ideal

gas that for simplicity is placed in a chamber with a piston, allowing for

volume changes (Figure 2.6). The volume change can be related to the

change in the pressure, temperature, and number of molecules:

(2.15)

Since the pressure and the amount of gas are assumed to be held constant,

only the temperature can change and the change in volume is proportional

to the change in temperature:

(2.16)

Substituting this expression into the relationship for ΔU(eqn 2.9) yields:

(2.17)

The heat flow can be related to the product of the specific heat at constant

pressure and temperature change, leading to the expression:

ΔU=q−nRΔT=CPΔT−nRΔT=(CP−nR)ΔT (2.18)

ΔΔUqPVqP Δ Δ

nR

P

=− =− TqnR

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟=− TT

ΔΔV Δ

nRT

P

nR

P

= T

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟=

ΔΔV

nRT

P

=

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟

32 PARTI THERMODYNAMICS AND KINETICS

Heat

Work

Figure 2.6For an
ideal gas the work
performed in moving
a piston is equal to
the change in heat.