Why is boyles law hyperbolic

Thus, for a given amount of the gas, the product of pressure and volume is constant at constant temperature. If V 1 and V 2 are the volumes of a gas at pressures P 1 and P 2 respectively at a constant temperature. Graphical Representation:. A graph is drawn by taking volume on the x-axis and pressure on the y-axis. The graph is as follows.

This graph is also known as PV diagram. Each curve is rectangular hyperbola and corresponds to a different constant temperature and is known as an isotherm constant temperature plot. Higher curves correspond to higher temperatures. It should be noted that volume of the gas doubles if pressure is halved. The graph parallel to x-axis confirms that at a particular temperature of the gas, the product of its volume and corresponding pressure is always constant.

Relation Between Density and Pressure:. Thus the density of the certain mass of an enclosed gas is directly proportional to its pressure. According to the kinetic theory of gases, gas consists of a large number of minute particles which are always in constant random motion. During this process, they collide with each other and with the walls of the container containing it. When molecules collide with the walls of the container, there is a change in the momentum of the colliding molecules.

This is the cause of the pressure of the gas. According to the kinetic theory of gases, the kinetic energy of molecules is directly proportional to the absolute temperature of the gas. Hence the kinetic energy of the molecules is a constant.

For enclosed gas, the number of molecules of a gas is constant. The graph of pressure vs inverse volume is a straight line passing through the origin and having the positive slope, k. The graph above is a straight line parallel to the x -axis. This proves the product of pressure and volume at a constant temperature and amount of gas is constant.

The lines in the graph are independent of volume or pressure. It is as follows: The curve is called PV curve, and it is hyperbolic in nature. Mathematical explanation Volume is on the x -axis and pressure, on the y -axis.

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