A gas undergoes a process from state $1,$ where $p_l=80l\frac{b_f}{i}{n}^2,v_l=4\mathrm{.}0f\frac{t^3}{l}b,$ to state $2$ where $p_2=10l\frac{b_f}{i}{n}^2,$ according to $p{v}^{1\mathrm{.}3}=$ constant. The relationship between pressure, specific volume, and internal energy is

$u=(0\mathrm{.}2651)pv-95\mathrm{.}436$

where $p$ is in $l\frac{b_f}{i}{n}^2,v$ is in $f\frac{t^3}{l}b,$ and $u$ is in $Bt\frac{u}{l}b.$ The mass of gas is $20$ lb $.$ Neglecting kinetic and potential energy effects. Determine the work done by the system and heat transfer to the system, in Btu.