Why is the rate inversely proportional to the square root of temperature in Grahams Law of Diffusion? In my book it is given that:


  The general form of the Grahams Law of Diffusion can be stated as follows when one or all of the parameters are varied:
  $$\text{rate} \propto \frac{PA}{\sqrt{TM}},$$
  where $P$ - pressure, $A$ - area of the hole, $T$ - temperature, $M$ - Molecular weight.


How can rate be inversely proportional to the square root of temperature? I feel that on increasing temperature it must increase, but how can the rate decrease?
Is the formula in my book correct or incorrect?
It helps to rewrite 
$$\text{rate} \propto \frac{PA}{\sqrt{TM}}$$
by assuming the ideal gas law holds, as follows:
$$\text{rate} \propto \frac{RA}{V_m}\sqrt{\frac{T}{M}}$$
where $V_m$ is the molar volume or inverse of molar particle density. 

Written this way it is clear that if the particles occupy the same volume, increasing their temperature increases the rate at which they effuse through the apperture.