In a pressure vs. volume graph, how is an adiabatic process represented?

An adiabatic process in a pressure vs. volume graph is represented by a curve that slopes down, not as a straight line. In an adiabatic process, no heat is exchanged with the surroundings, and the relationship between pressure and volume is governed by the principles of thermodynamics.

During an adiabatic expansion, the gas does work on the surroundings, which results in a decrease in internal energy and, consequently, pressure. This relationship can be described mathematically by the equation (PV^\gamma = \text{constant}), where (P) is pressure, (V) is volume, and (\gamma) is the heat capacity ratio (C_p/C_v). The result of this equation indicates that as the volume increases, the pressure decreases at a rate that is not linear, hence the curve's slope decreasing in a non-linear fashion on the graph.

This characteristic shape differentiates it from other types of processes, such as isothermal processes, which may appear as different slopes or shapes on the graph. The specific curvature of the line in the pressure vs. volume graph indicates the nature of the gas's response to volume changes under adiabatic conditions, distinctly illustrating the lack of heat transfer.