Determine $($a$)$ the specific volume and $($b$)$ the density of $20$ kg of methane gas contained in a $20m^3$

tank$.$ The gage pressure of the methane is $61\mathrm{.}2$ kPa and the methane is in thermal equilibrium with

the surroundings. The temperature and the absolute pressure of the surroundings in which the tank

exists are $40C$ and $100$ kPa $,$ respectively.

During January in Montana, the temperature on the Celsius scale reads identical to the temperature

on the Fahrenheit scale. $($a$)$ What is this temperature? $($b$)$ What is this temperature in K$?($c$)$ What is

this temperature in $R?$

In order to fly, the thoracic temperature of a butterfly must be between $97F$ and $104F.$ Determine

the size of this temperature range $(7F)$ in $K,C,$ and R $.$ Does the size of this range differ when

measured in relative or absolute units?

A secret gas is confined in a flexible container. The pressure and specific volume are $1$ MPa and $0\mathrm{.}5$

$\frac{m^3}{k}g.$ The gas expands to a new pressure of $250$ kPa $.$ The relation between pressure and specific

volume is $P{v}^{1\mathrm{.}4}=$ constant. Determine the specific volume at the $250$ kPa $.$

A piston$-$cylinder assembly containing a gas goes through the following processes:

a$.1-2$: Beginning at $P_1=1$ bar and $V_1=1\mathrm{.}0m^3,$ the gas is compressed to $V_2=0\mathrm{.}2m^3.$ The

compression process is described by: $pV=$ constant

b$.2-3$: Constant$-$pressure expansion to $V_3=1\mathrm{.}0m^3$

c$.3-1$ : The volume remains constant.

Graph these processes on a $p-V$ diagram. Label the pressure and volume values at each numbered

state.

A $1100$ kg automobile moves at a constant speed of $45k\frac{m}{h}r.($a$)$ Determine the kinetic energy of

the automobile. $($b$)$ If the automobile accelerates to $75k\frac{m}{h}r,$ what is the change in kinetic energy

of the automobile?

Tabulated below is information about $5$ different processes that occur in a closed system. Fill in the

blank spaces. Assume all units are the same.

One kg of gas is compressed $($i$.$e$.,$ its volume is reduced$)$ by cooling at a constant pressure of $400$

kPa $.$ The reduction in gas volume results in an energy transfer to the system of $168$ kJ in the form of

boundary work. If the initial specific volume is $0\mathrm{.}72\frac{m^3}{k}g,$ what is the final volume of the gas in $m^3?$

Use thermodynamics to solve and please make steps clear and neat. Will Like if work is done!