E1.1 You are working on an experimental fission reactor that is fueled by deuter
ID: 2306052 • Letter: E
Question
E1.1 You are working on an experimental fission reactor that is fueled by deuterium. The deuterium gas is very valuable and is delivered in ?? = 1 liter tanks, as shown in the figure below. You would like to transfer as much of the deuterium that is initially in the tank to your experiment as possible. The initial temperature of the tank is ???????? = 20°C and the initial pressure is ??????????,???????? = 15 psig (i.e., pounds per square inch gage pressure). The experiment is always maintained at pressure ????????,???????? = 5 psig (also a gage pressure). The atmospheric pressure is ???????? = 1 atm.
You should model deuterium as an ideal gas for this problem; the ideal gas law relates pressure, temperature, and specific volume according to: ?? = ????/ ?? where ?? = 2064 J/kg-K is the ideal gas constant for deuterium and ?? and ?? are the absolute temperature and pressure.
a) Determine the absolute pressure of the deuterium initially in the tank and the absolute pressure of the deuterium in the experiment (in Pa). Initially, the valve connecting the tank to the experiment is opened and deuterium flows from the tank to the experiment until the pressure in the tank reaches ????????. (Note that the pressure in the experiment does not change during this process). The temperature of the tank remains at ???????? during this process due to heat transfer with the surroundings.
b) Determine the mass of deuterium that passes from the tank to the experiment.
c) Determine the fraction of the mass of deuterium that is initially in the tank that passes to the experiment during this process. In order to get an additional transfer of deuterium from the tank to the experiment you have decided to heat the tank to ????????? = 50°C while the valve remains open. The tank is connected to the experiment during this process so that the pressure in the tank remains at ????????.
d) Determine the mass of deuterium that passes from the tank to the experiment during the heating process.
e) Determine the total fraction of the mass of deuterium initially in the tank that is transferred to the experiment during the entire process.
f) Plot the total fraction of the mass of deuterium that is initially in the tank that is transferred to the experiment during the entire process as a function of the temperature of the tank at the conclusion of the heating process for 20°C < ????????? < 100°C. In 1 to 3 sentences, explain (in a comment) how and why the total fraction changes with temperature.
mental fission reactor that is fueled b V 1 liter tanks, as shown in the fi is initially in the tank to your experi to experiment at Pexp.gegge 5 psig n tank, 1 liter Tini 20°C fill,gage = 15 psig i 20°C and the initial pressure i The experiment is always maintai . Y gas law relates pressure, temperatu in pheric pressure is Patm 1 atm RTExplanation / Answer
E1.1
experimental fission reactor fueled by Deuterium
V = 1 l tanks
Ti = 20 C
Pi = 15 psig = 103421 Pa + 1.01*10^5 Pa = 2.04421 *10^5Pa
Pe = 5 psig = 34473.8 + 1.01*10^5 = 1.354738 *10^5 Pa
Pa = 1 atm = 1.01*10^5 Pa
a. initially abbsolute prtessure of deuterium in the tank = Po = 1.0789476*10^5 Pa
and absolute pressure in the experiment , Pe = 1.354738*10^5 Pa
now, temepratue rof the tank remains constant
Ti = 20 C = 293.16 K
b. mass of deuterium passing = m
now
initial number of moles = ni
final numebr of moles = nf
molar mas sof deuterioum = M
hence
m = (ni - nf)M
now,
Pi*V = ni*RTi
Pf*V = nf*RTi
m = (PiV/RTi - PfV/RTi)*M = M*V(Pi - Pf)/RTi
m = 0.002*1*10^-3(2.04421 - 1.354738)*10^5/8.31*293.16
m = 0.0566031 g
c. mi = ni*M = M*V(Pi)/RTi = 0.1678 g
hence
m/mi = 0.33727
d. Tf = 50 C = 323.16 K
due to heating
nf' = Pf*V/RTf = 0.050447156 mol
additional mass removed due to heating = (nf - nf')*M = 0.010324 g
e. total fraction = (m + m')/mi = 0.398855
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