PROBLEM $3-$ ENERGY CONSERVATION

For the system above and where $n=1\mathrm{.}4,$ if the mass of the gas$/$vapor in the cylinder is $2\mathrm{.}0$ kg $,$ answer the

following:

a$)$ Write down the conservation of energy equation, and state your assumptions to simplify the equation.

b$)$ Sketch the problem schematic and identify your system of interest.

c$)$ What is the value of $p$ at state $2?$

d$)$ If the vendors who sell this piston$-$cylinder device claim it is adiabatic $($i$.$e$.,$ no heat transfer$),$ where does

the work done due to compression go$?$ How much is this work of compression?

e$)$ Now, if the device is actually not perfectly adiabatic and you find this out by doing a measurement for

the change in internal energy of the gas$/$vapor inside the cylinder $($you measure $u=66\mathrm{.}667k\frac{J}{k}g$ for the

gas$/$vapor$).$ What is the equivalent heat transfer coefficient $(h,\frac{J}{m^2}*K)$ if the heat is lost due to natural

convection to the ambient at $22C?$ The cylinder has a radius of ~~$0\mathrm{.}8m$ and the gas$/$vapor volume occupies a

length$/$height of ~~$0\mathrm{.}75m$