## Pressure Formula – Pressure Equation

**Pressure** is a measure of the **force exerted** per unit area on the boundaries of a substance. The standard unit for **pressure** in the SI system is the **Newton per square meter or pascal (Pa)**. Mathematically (pressure formula):

**p = F/A**

where

**p is the pressure****F is the normal force****A is the area of the boundary**

Pascal is defined as force of 1N that is exerted on unit area.

**1 Pascal = 1 N/m**^{2}

**kPa**, the

**bar**, and the

**MPa**.

**1 MPa 10**^{6}N/m^{2}**1 bar 10**^{5}N/m^{2}**1 kPa 10**^{3}N/m^{2}

In general, pressure or the force exerted per unit area on the boundaries of a substance is caused by the **collisions** of the **molecules** of the substance with the boundaries of the system. As molecules hit the walls, they exert forces that try to push the walls outward. The forces resulting from all of these collisions cause the **pressure** exerted by a system on its surroundings. Pressure as an **intensive variable** is constant in a closed system. It really is only relevant in liquid or gaseous systems.

## Ideal Gas Law

Any equation that relates the pressure, temperature, and specific volume of a substance is called an **equation of state**. The simplest and **best-known** equation of state for substances in the gas phase is the **Ideal Gas equation** of state. It was first stated by Émile Clapeyron in 1834 as a combination of the empirical Boyle’s law, Charles’ law and Avogadro’s Law. This equation predicts the **p-v-T behavior** of a gas quite accurately for dilute or low-pressure gases. In an ideal gas, molecules have no volume and do not interact. According to the ideal gas law, pressure varies linearly with** temperature** and **quantity**, and inversely with **volume**.

*pV = nRT*

where:

is the*p***absolute pressure**of the gasis the*n***amount**of substanceis the*T***absolute temperature**is the*V***volume**is the ideal, or universal,*R***gas constant**, equal to the product of the Boltzmann constant and the Avogadro constant,

In this equation the symbol R is a constant called the **universal gas constant** that has the same value for all gases—namely, **R = 8.31 J/mol K.**

The power of the ideal gas law is in its **simplicity**. When any** two** of the thermodynamic variables, p, v, and T** are** **given**, the **third** can **easily be found**. An ideal gas is defined as one in which all collisions between atoms or molecules are perfectly elastic and in which there are no intermolecular attractive forces. An ideal gas can be visualized as a collection of perfectly hard spheres which collide but which otherwise do not interact with each other. In reality, no real gases are like an ideal gas and therefore no real gases follow the ideal gas law or equation completely. At temperatures near a gases boiling point, increases in pressure will cause condensation to take place and drastic decreases in volume. At very high pressures, the intermolecular forces of a gas are significant. However, most gases are in approximate agreement at pressures and temperatures above their boiling point. The ideal gas law is utilized by engineers working with gases because it is simple to use and approximates real gas behavior.

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