ABSTRACT
If the heat …ow is constant, entropy is produced in this composite system at a rate
d d Q S t
I T T
= − ⎛
⎝
⎜
⎞
⎠
⎟
1 1 2 1
,
(20.1)
where IQ = dQ/dt is the heat current with the unit joules per second. As an approximation, if T1 ≈ T2, we introduce an average temperature T = (T1 + T2)/2 and with the system not far from equilibrium, Equation 20.1 becomes
d d Q S t
I T T
=
Δ
2 , (20.2)
where ΔT = T1 - T2. For convenience, an entropy current Is = IQ/T may be deˆned in terms of the heat current, giving
d d S S t
I T T
=
Δ
(20.3)
Provided the heat baths have suªciently large heat capacities so that ΔT remains approximately constant, entropy will continuously be produced at the rate given by Equation 20.3. e form of Equation 20.3, which applies to thermal energy …ow, may be generalized to allow for coupled …ows that involve, for example, energy and particles. is development is dealt with in the next section, ˆrst for the cases of discrete systems that consist of distinct parts and second for continuous systems such as a bar through which both heat and charge …ow.
