gas. The equation ( . ) gives the connection between the macroscopic world (temperature) to microscopic world (motion of molecules). (ii) The average kinetic energy of each molecule depends only on temperature of the gas not on mass of the molecule.
In other words, if the temperature of an ideal gas is measured using thermometer, the average kinetic energy of each molecule can be calculated without seeing the molecule through naked eye. By multiplying the total number of gas molecules with average kinetic energy of each molecule, the internal energy of the gas is obtained. Internal energy of ideal gas U N mv By using equation ( . ) U NkT = ( .
) From equation ( . ), we understand that the internal energy of an ideal gas depends only on absolute temperature and is independent of pressure and volume. EXAMPLE . A football at °C has .
mole of air molecules. Calculate the internal energy of air in the ball. Solution The internal energy of ideal gas = NkT . The number of air molecules is given in terms of number of moles so, rewrite the expression as follows - - - - Unit Kinetic theory of gases From equation ( .
) N V m v N V m v ( . ) where v and v are the mean square speed for two gases and N and N are the number of gas molecules in two different gases. At the same temperature, average kinetic energy per molecule is the same for two gases. m v m v ( .
) Dividing the equation ( . ) by ( . ) we get N = N This is Avogadro’s law. It is sometimes referred to as Avogadro’s hypothesis or Avogadro’s Principle.
. . Root mean square speed ( v rms ) Root mean square speed ( v rms ) is defined as the square root of the mean of the square of speeds of all molecules. It is denoted by v rms = v Equation ( .
) can be re-written