As a result of a certain process the viscosity coefficient of an ideal gas increases `alpha=2.0` times and its diffusion coefficient `beta = 4.0` times. How does the gas pressure change and how many times ?

Explanation

We know
`eta = (1)/(2) lt v gt lamda rho = (1)/(3) lt v gt (1)/(sqrt(2) pi d^2) m alpha sqrt(T)`
Thus `eta` changing `alpha` times implies `T` changing `alpha^2` times.
On the other hand
`D = (1)/(3) lt v gt = (1)/(3) sqrt((8 kT)/(pi m)) (kT)/(sqrt(2) pi d^2 p)`
Thus `D` changing `beta` means `(T^(3//2))/(p)` changing `beta` times
So `p` must change `(alpha^3)/(beta)` times.