$3\mathrm{.}111($Moran $8^{th}$ edition$)$ A piston$-$cylinder device

assembly fitted with a paddle wheel contains air,

initially at $p_1=30lb\frac{f}{i}{n}^2,T_1=540F,$ and $V_1=4f{t}^3.$

The air undergoes a process to a final state where

$p_2=20lb\frac{f}{i}{n}^2,V_2=4\mathrm{.}5f{t}^3.$ During the process, the

paddle wheel transfer energy to the air by work in the

amount of $1$ Btu $,$ and there is energy transfer to the air

in the device by heat in the amount of $-12$ Btu.

Assuming ideal gas behavior, and neglecting kinetic

and potential energy effects, determine for the air:

a$)$ The temperature at state $2(R)$

b$)$ The energy transfer by work by the air in the piston

$($Btu$)$

Fig. P$3.111$