# Info

The compression in the experiment starts from 1 MPa (when the gas volume was 100 liters) and ends when the pressure reaches 10 MPa (at a volume of 19.3 liters).

In the case of the abrupt compression, the initial state, (A), is the same as in the previous case. The final state, (B), has the same pressure (10 MPa) as before, but since the gas is at a higher temperature, the volume is larger (35.7 liters versus 19.3 liters). However, the path from one state to the other is unknown, a fact indicated by the dotted line. During such a rapid compression, the pressure and the temperature cannot be specified because they are not uniform throughout the mass of the gas. As the piston presses down, the gas piles up in the vicinity of the piston, not having time to spread out uniformly.

The terms gradual and abrupt are relative. In most machines, even at high-speed operation, the compression (or expansion) can be taken (with little error) as gradual.

### 2.9.4 Polytropic Law

Assume that the cylinder with piston used in our discussion of the pressure-volume work is insulated so that no heat can be exchanged between the gas inside and the environment outside. We have adiabatic conditions, and the heat exchanged is dQ = 0. (2.39)

Consider an infinitesimal step in the compression process. The work is dW = p dV. (2.40) From the first law of thermodynamics, we have dQ = dU + dW = 0. (2.41) and from the perfect-gas law,