# How do you simplify for Q+w=m(h1-h2)?

So, I'm given the following equation: $$\frac{∂Q}{∂t}+\frac{dm_i}{dt}(E_i+P_iV_i)=\frac{dE}{dt}+\frac{dm_{fi}}{dt}(E_f+P_fV_f)-\frac{∂W_s}{∂t}$$

Using that equation, I am supposed to then simplify it into $$\overset{.}Q+\overset{.}W=\overset{.}m(h_1-h_2)$$ However, I don't know how to start, and so far I haven't found anything similar that I can use as a basis.

• It wouldn't hurt if you define every variable in the posted equation, too. I'm pretty sure you are using inconsistent labelling, e.g. with "f", "2" and "fi" for "final", and the derivative shouldn't be a variable. A general note: in chemistry and physics, boldface usually refers to a vector. Mar 9 '21 at 16:03
• Please rewrite ! Write $E$ instead of $e$, $H$ instead of $h$. Write $dt$ instead of $d_t$. Write the indexes as proposed by Andselisk. Explain what is $m$ ! Write $dE$ instead of $E_{t+dt}$- $E_t$ Explain why the mass and the work are supposed to change in time. Mar 9 '21 at 21:11