$4\mathrm{.}19.$ Reversible compression of $1$mol of an ideal gas in a piston$/$cylinder device results in a pressure increase from $1$ bar to $P_2$ and a temperature increase from $400K$ to $950K.$ The path followed by the gas during compression is given by $P{V}^{1\mathrm{.}55}=$ const, and the molar heat capacity of the gas is given by:

$]=[K$

Determine the heat transferred during the process and the final pressure.