(4) Starting from the equation of state for ideal gas (1 mol, pV = RT), show that the following (Joule's law) is true: au = 0 av T
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- For an ideal gas held at room temperature (293 K), if the pressure is changed from 2 atm to 8 atm, the volume wil quadruple double stay the same be 1/4 as much(1) Consider 1 mol of an ideal gas at 300 K and 1 atm pressure. Imagine that the molecules are, for the most part, evenly spaced at the centers of identical cubes. Using Avogadro's constant and taking the diameter of a molecule to be 3 x 10-8 cm, find the length of an edge of such a cube and calculate the ratio of this length to the diameter of a molecule. The edge length is an estimate of the distance between molecules in the gas. (2) Now consider a mole of water having a volume of 18 cm³. Again, imagine the molecules to be evenly spaced at the centers of identical cubes and repeat the calculation in (a).For a dilute gas of N monatomic particles with mass m and total energy E, use the Sackur- Tetrode equation for the entropy S V = log + NkB to derive expressions for the pressure and internal energy in terms of the temperature T and volume V. [You may use that X₁ = 3πh² N/(mE).] th