Assumptions to be taken when rearranging terms in first law of thermodynamics
This equation can not be applied in general because it can't describe the amount of heat transferred to an incompressible solid or liquid at constant pressure.
For these cases, it would predict that $\mathrm dQ=0$ (which is not necessarily correct).  If it is not generic, it also cannot describe real gases beyond the ideal gas region.  Therefore, the equation must apply exclusively to an ideal gas. The presence of the ideal gas constant $R$ in the equation is a dead giveaway.
For a reversible path,
$$\mathrm dQ=T\mathrm dS=C_v\mathrm dT+P\mathrm dV$$
But, for an ideal gas,
\begin{align}
&amp;\mathrm dT =\frac{P\mathrm dV+V\mathrm dP}{R}\\
&amp;C_v+R = C_p
\end{align}
Therefore,
\begin{align}\mathrm dQ&amp;=C_v\frac{P\mathrm dV+V\mathrm dP}{R}+P\mathrm dV \\ &amp;=\frac{C_v}{R}V\mathrm dP+\frac{(C_v+R)}{R}P\mathrm dV \\
\implies\mathrm dQ&amp;=\frac{C_v}{R}V\mathrm dP+\frac{C_p}{R}P\mathrm dV
\end{align}
This equation applies only to an ideal gas and a reversible path.