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For example, the ideal gas law in terms of the Boltzmann constant is: =, where N is the number of particles (molecules in this case), or to generalize to an inhomogeneous system the local form holds: =, where n = N/V is the number density. Finally, by defining the kinetic energy associated to the temperature:
How much gas is present could be specified by giving the mass instead of the chemical amount of gas. Therefore, an alternative form of the ideal gas law may be useful. The chemical amount, n (in moles), is equal to total mass of the gas (m) (in kilograms) divided by the molar mass, M (in kilograms per mole): =.
where P is the pressure of the gas, V is the volume of the gas, and k is a constant for a particular temperature and amount of gas.. Boyle's law states that when the temperature of a given mass of confined gas is constant, the product of its pressure and volume is also constant.
We can solve for the temperature of the compressed gas in the engine cylinder as well, using the ideal gas law, PV = nRT (n is amount of gas in moles and R the gas constant for that gas). Our initial conditions being 100 kPa of pressure, 1 L volume, and 300 K of temperature, our experimental constant (nR) is:
The table below displays densities and specific volumes for various common substances that may be useful. The values were recorded at standard temperature and pressure, which is defined as air at 0 °C (273.15 K, 32 °F) and 1 atm (101.325 kN/m 2, 101.325 kPa, 14.7 psia, 0 psig, 30 in Hg, 760 torr). [4]
If mass density is ρ, the mass of the parcel is density multiplied by its volume m = ρA dx. The change in pressure over distance dx is dp and flow velocity v = dx / dt . Apply Newton's second law of motion (force = mass × acceleration) and recognizing that the effective force on the parcel of fluid is −A dp.
Classical mechanics is the branch of physics used to describe the motion of macroscopic objects. [1] It is the most familiar of the theories of physics. The concepts it covers, such as mass, acceleration, and force, are commonly used and known. [2] The subject is based upon a three-dimensional Euclidean space with fixed axes, called a frame of ...
For the special case of a gas to which Boyle's law [4] applies, the product pV (p for gas pressure and V for gas volume) is a constant if the gas is kept at isothermal conditions. The value of the constant is nRT, where n is the number of moles of the present gas and R is the ideal gas constant. In other words, the ideal gas law pV = nRT ...