# GATE2014-26

The concentration profile of a chemical at a location $x$ and time $t$, denoted by $c(x,t)$, changes as per the following equation,

$$c(x,t)=\frac{c_0}{\sqrt{2\pi Dt}}\exp[-\frac{x^2}{2Dt}]$$

where $D$ and $c_0$ are assumed to be constant. Which of the following is correct?

1. $\frac{\partial c}{\partial t}=D\frac{\partial^2 c}{\partial x^2}$
2. $\frac{\partial c}{\partial t}=\frac{D}{2}\frac{\partial^2 c}{\partial x^2}$
3. $\frac{\partial^2 c}{\partial t^2}=D\frac{\partial^2 c}{\partial x^2}$
4. $\frac{\partial^2 c}{\partial t^2}=\frac{D}{2}\frac{\partial^2 c}{\partial x^2}$
in Others
edited

## Related questions

1
The unit for specific substrate consumption rate in a growing culture is $\frac{g}{L-h}$ $\frac{g}{h}$ $\frac{g}{g-h}$ $\frac{gmoles}{L-h}$
2
Since mammalian cells are sensitive to shear, scale-up of a mammalian cell process must consider, among other parameters, the following $\text{(given N=rotations/time, D=diameter of impeller)}$ $\pi ND$ $\pi N^2D$ $\pi ND^2$ none of these
A bacterium belonging to cocci group has a diameter of $2\:\mu m.$ The numerical value of the ratio of its surface area to volume (in $\mu m^{-1}$) is _______.
The statistical frequency of the occurrence of a particular restriction enzyme cleavage site that is $6$ bases long can be estimated to be once every $24$ bases once every $256$ bases once every $1024$bases once every $4096$ bases