As a result of some process the pressure of an ideal gas increases `n-fold`. How many times have the mean free path `lamda` and the number of collisions of each molecule per unit time `v` changed and how, if the process is
(a) isochoric ,
(b) isothermal ?

Explanation

(a) In an isochoric process `lamda` is constant and
`v alpha sqrt(T) alpha sqrt(p V) alpha sqrt(p) alpha sqrt(n)`
(b) `lamda = (kT)/(sqrt(2) pi d^2)` must decrease `n` times in an isothermal process and `v` must increase `n` times because `ltvgt` is constant in an isothermal process.