QUESTION $1$

$1\mathrm{.}1.$ A gas contains a volume of $0\mathrm{.}055m^3$ expands polytropically from a pressure of

$32$ bar to $3$ bar. The polytropic expansion $n=1\mathrm{.}3.$ Calculate:

$1\mathrm{.}1\mathrm{.}1.$ The final volume.

$1\mathrm{.}1\mathrm{.}2.$ The work done by gas during the expansion.

$1\mathrm{.}2.$ A mass of $4\mathrm{.}3kg$ of gas enclosed in cylinder$-$piston assembly is allowed to

expand in accordance with $P{V}^2=C$ where upon its initial state $0\mathrm{.}22m^3$ at $5$

bar changes to a final pressure of $2$ bar. Assuming the expansion to be quasi$-$

static, given the specific internal energy changes in accordance with $U=2\mathrm{.}88$

$PV+90.$ Calculate:

$1\mathrm{.}2\mathrm{.}1.$ The change in internal energy.

$1\mathrm{.}2\mathrm{.}2.$ The work done.

$1\mathrm{.}2\mathrm{.}3$ The heat.