PLEASE WORK AND EXPLAIN REASONING FOR PARTS D$-$G

$(7$ points$)$ Gas is trapped inside a rigid cylinder. A piston inside the cylinder can move to change the

volume of the trapped gas. The mass of gas inside the cylinder is $0\mathrm{.}3008$ lb m $.$ The initial volume is $4f{t}^3,$ the

initial pressure is $14\mathrm{.}696$ psia $,$ and the initial temperature is $68F.$

The piston is then moved to compress the gas to a volume of $0\mathrm{.}75f{t}^3.$ Previous experiments with this

apparatus have shown that this compression process can be modeled as a polytropic process with a

polytropic exponent of $1\mathrm{.}3..$

During the compression, heat transfer from the gas to the surroundings through the cylinder wall is

measured to be $5\mathrm{.}71$ Btu.

Determine the following. Round your answers to three significant figures.

a$.$

$13\mathrm{.}3$

$f\frac{t^3}{l}bm$

Initial specific volume of the gas

$13\mathrm{.}29787234$

b$.$

$I\frac{b}{f}{t}^3$

Final density of the gas

$0\mathrm{.}401066667$

Final absolute pressure of the gas

$129,5082663$

c$.$

psia

d$.-5\mathrm{.}71$

Btu

e$.-18,400$

$ft-lbf$

f$.-23\mathrm{.}7$

Btu

Btu

Energy flowing into the gas due to heat transfer $($Q$)$

Work done by the gas on the piston $($W$)-18,406\mathrm{.}65587$

Work done by the gas on the piston $($W$)-23\mathrm{.}65377214$

Change in internal energy of the gas $(U)+17\mathrm{.}94377214$