Problem Set #$4($Chapter $3$ Part $2)$

A $100-L$ container is filled with $1$ kg of air at a temperature of $24\mathrm{.}70C.$ What is

the pressure in the container? The gas constant of air is $R=0\mathrm{.}287k\frac{J}{k}g*K.$

A spherical balloon with a diameter of $9$ m is filled with helium at $29\mathrm{.}00C$ and

$200$ kPa $.$ Determine the mole number and the mass of the helium in the balloon.

The universal gas constant is $Ru=8\mathrm{.}314$kPa$*\frac{m^3}{k}$mol$*K.$ The molar mass of

helium is $4\mathrm{.}0k\frac{g}{k}$mol.

A mass of $0\mathrm{.}1$ kg of helium fills a $0\mathrm{.}2m^3$ rigid vessel at $350$ kPa $.$ The vessel is

heated until the pressure is $770$ kPa $.$ Calculate the temperature change of helium

$($in K$)$ as a result of this heating. The gas constant of helium

is $R=2\mathrm{.}0769$kPa$*\frac{m^3}{k}g*K.$

The refrigerant$-134$a is in vapor state at $0\mathrm{.}9$ MPa and $70C.$ The gas constant,

the critical pressure, and the critical temperature of refrigerant$-134$a

are: $R=0\mathrm{.}08149$kPa$*\frac{m^3}{k}g*K,Tcr=374\mathrm{.}2K,$ and $Pcr=4\mathrm{.}059$MPa.

$(1)$ Determine the specific volume of refrigerant$-134$a based on the property

tables.

$(2)$ Determine the specific volume of refrigerant$-134$a based on the ideal$-$gas

equation.

$(3)$ Determine the specific volume of refrigerant$-134$a based on the generalized

compressibility chart.

$(4)$ Compute the percent error for the last two methods.

A rigid tank contains $2$ kg of an ideal gas at $4$ atm and $40C.$ Now a valve is

opened and half of mass of the gas is allowed to escape. If the final pressure in

the tank is $2\mathrm{.}2$ atm $,$ determine the final temperature in the tank.

$($answer: $71C)$