Lecture-Notes (Thermodynamics) - niser

4.2. SECOND LAW OF THERMODYNAMICS 27
2. B → C: adiabatic expansion, during which
and
while δQ = 0.
T1 → T2
VB → VC,
3. C → D: isothermal compression at T = T2; the system ejects heat Q2 to the bath
(Q2 < 0 is a convention).
4. D → A: adiabatic compression, during which
T2 → T1,
VD → VA,
δQ = 0.
In one cycle operation, the system receives an amount of heat Q1 from a hot reservoir,
performs work, and rejects ”waste heat” Q2 to a cold reservoir.
From the first law of thermodynamics we have:
0 = dU = (δQ + δW) = Q + W = Q1 + Q2 + W,
where −W is the work performed by the system, equal to the area enclosed in the loop
(shaded area in Fig. 4.4).
The efficiency of the Carnot engine is defined as
η ≡
performed work
absorbed heat
= −W
Q1
= Q1 + Q2
Q1
= Q1 − |Q2|
Q1
η is 100% if there is no waste heat (Q2 = 0). However, we will see that this is impossible
due to the second law of thermodynamics.
4.2 Second law of thermodynamics
Definition by Clausius:
” There is no thermodynamic transformation whose sole effect is to deliver heat
from a reservoir of lower temperature to a reservoir of higher temperature.”
Summary: heat does not flow upwards.
Definition by Kelvin:
”There is no thermodynamic transformation whose sole effect is to extract heat
from a reservoir and convert it entirely to work”.
Summary: a perpetuum mobile of second type does not exist.
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