11.4.3 P-V Diagram

The most popular “system” in A-level physics is an ideal (monatomic) gas contained in a cylinder with a frictionless piston. As a system, the state of the gas is defined by its state variables (pressure, volume and temperature). When changing from one state to another, the system traverses through many in-between states. The path taken by the gas is called a thermodynamic process.

Thermodynamics processes are often represented using something known as the P-V diagram. Also called the indicator diagram, it was invented by James Watt in the 1780s to evaluate the performance of his steam engines. It is basically a chart that records the pressure of steam versus the volume of steam in a cylinder. The way he generated the chart was quite cute: he attached a board to the piston, and a pencil to the pressure gauge needle. As the steam engine goes through its cycles, the piston moves left and right and pressure gauge needle rises and falls, and ta-dah the P-V diagram is traced out automatically by the pencil on the board.

Notice that the temperature of the system is not directly displayed in a P-V diagram. For this reason, we often overlay a series of isotherms on a P-V diagram (drawn in dashed lines in the P-V diagram below).

Isotherms are lines of constant temperature. For an ideal gas, this means \displaystyle p=\frac{{nRT}}{V}=\frac{{\text{constant}}}{V} . This is why all isotherms are \displaystyle \frac{1}{x}  curves on a P-V diagram. The higher the temperature, the higher the isotherm sits in the P-V diagram.

For example, in the above P-V diagram, we can tell that the temperature was increasing during BCD (T1 to T2 to T5) but decreasing during DAB (T5 to T3 to T1).

Concept Test

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