For a gas obeying the ideal gas law, we can write p=f(v, t), v=g(p, t), and t=h(p, v). verify the validity of the cyclic rule by evaluating the following product for an ideal gas: (∂p∂v)t(∂v∂t)p(∂t∂p)v and express your answer in terms of the ideal gas law parameters.

The size (radius) of an oxygen molecule is about 2.0 ×10−10m. make a rough estimate of the pressure at which the finite volume of the molecules should cause noticeable deviations from ideal-gas behavior at ordinary temperatures (t= 300k ). assume that deviatons would be noticeable when volume of the gas per molecule equals the volume of the molecule itself.