The Second Law

Second law: It is impossible to construct a device that operates in cycles that converts heat into work without producing some other change in the surroundings.

Figure 1. A thermodynamic cycle

Consider an idealized cycle. In this cycle there are the following four steps

  1. Isothermal expansion
  2. Adiabatic expansion
  3. Isothermal compression
  4. Adiabatic compression

This is known as a Carnot cycle.

 

Clearly, the volume ratios at points 1, 2, 3, and 4 are established by

so that

The heat q for the adiabatic steps is zero.

Therefore,

For the isothermal steps. The red curve represents the isothermal expansion (hot gas) and the blue curve represents the isothermal compression (cold gas). Since these processes are isothermal we know that

DU = 0 and qtotal = -wtotal.

The total work of isothermal expansion and compression is given by

Note that V2 > V1 and so whot < 0 represents work done by the system.

Note that V4 < V3 and so wcold > 0 represents work done on the system.

Note also that qtotal = -wtotal ¹ 0 and neither heat nor work is a state function.

Since

And furthermore V4/V3 = V1/V2 we have

which means that

The latter equation is very important since it defines a thermodynamic temperature scale. The ratio of the temperatures is equal to the ratio of the heats transferred

Note further that we define the thermodynamic efficiency as

The entropy change for the system can be calculated by

DS = nRln(V2/V1) constant T

DS = nCvln(T2/T1) constant V

DS = nCpln(T2/T1) constant P