Derive \dot v: A Thermo Relation for V, m and v

[An1MuS]

I'd like to know the result of deriving both sides of the equation in respect to time

$v= \frac {V}{m}$

$\frac {d}{dt}v=( \frac {d}{dt}) \frac {V}{m}$

which gives

$\dot v = . . . ?$

If you want some backup, this is a very common thermodynamics relation, where V = volume, m = mass and v = specific volume [m³/kg]. In open systems, we want to know mass flow and volumetric flow so we get $\dot m$ [kg/s] and $\dot V$ [m³/s]. I'd like to know if there's such a thing about specific volume as well, and that depends on how you do that derivative.

Best wishes and thanks,

An1MuS

 

[mathman]

The quotient rule applies: dv/dt = {mdV/dt - Vdm/dt}/m²