A shipment from Earth to Mars contains a 60 gallon [gal] tank filled with an ideal gas. The molecular weight of the ideal gas i
1 answer:
The ideal gas equation can find the amount of gas lost is 7 mol
Given parameters
- The initial and final pressures P1 = 3 atm and P2 = 2.2 atm
- The temperature T = 20ºC
- Container volume V = 60 gallon
To find
- The moles of gas lost
The intentional system of measurements (SI) is a system that determines which are the fundamental units, this allows to carry out calculations and exchange measurements in a uniform way and without errors, let's reduce the magnitudes to the SI system
P₁ = 3 atm (1 10⁵ Pa / 1 atm) = 3 10⁵ Pa
P₂ = 2.2 atm (1 10⁵ / 1 atm) = 2.2 10⁵ Pa
PM = 15.9 g / mol (1 kg / 1000 g) = 15.9 10⁻⁻³ kg / mol
V = 60 gallon (1 m³ / 264.172 gal) = 0.2271 m³
T = 20 + 273.15 = 293.15 K
Ideal gases are gases that have no interactions between them, so they can be described by the equation
PV = n R T
Where P is the pressure, V the volume, n the number of moles, R the ideal gas constant (R = 8.314 ) and T the temperature.
Let's look for the initial moles, that is, on Earth
n =
n =
n = 27.95 mol
Let's write the ideal gas equation for the two instants let's use subscript 1 for Earth and subscript 2 when the spacecraft is on Tuesday
P₁ V = n₁ R T
P₂ V = n₂ R T
n₂ =
n₂ =
n₂ = 20.95 mol
This is the amount of moles left, the moles lost are
n_ {lost} = n₁ -n₂
n_ {lost} = 27.95 - 20.95
n_ {lost} = 7 mol
Using the ideal gas equation we can find the amount of gas lost is 7 mol
Learn more about ideal gas here:
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Answer:
Explanation:
The question can be well structured in a table format as illustrated below:
Tensile Strength (MPa) Number- Average Molecular Weight (g/mol)
82 12,700
156 28,500
The tensile strength and number-average molecular weight for two polyethylene materials given above.
Estimate the number-average molecular weight that is required to give a tensile strength required above. Using the data given find TS (infinity) in MPa.
<u>SOLUTION:</u>
We know that :
where;
= Tensile Strength
= Tensile Strength (Infinity)
= Number- Average Molecular Weight (g/mol)
SO;
From equation (1) ; collecting the like terms; we have :
From equation (2) ; we have:
So;
Then;
Solving by L.C.M
By cross multiplying ; we have:
Collecting like terms ; we have
Dividing both sides by 15800:
A = 1695208.861
From equation (1);
Replacing A = 1695208.861 in the above equation; we have:
From equation(2);
Replacing A = 1695208.861 in the above equation; we have:
We are to also estimate the number- average molecular weight that is required to give a tensile strength required above.
If the Tensile Strength (MPa) is 82 MPa
Definitely the average molecular weight will be = 12,700 g/mol
If the Tensile Strength (MPa) is 156 MPa
Definitely the average molecular weight will be = 28,500 g/mol
But;
Let us assume that the Tensile Strength (MPa) = 181 MPa for example.
Using the same formula:
Then:
Collecting like terms ; we have:
1695208.861= 34.481
Dividing both sides by 34.481; we have:
=
Answer:
a. which is constant therefore, n = constant
b. The temperature at the end of the process is 109.6°C
c. The work done by the balloon boundaries = 10.81 MJ
The work done on the surrounding atmospheric air = 10.6 MJ
Explanation:
p₁ = 100 kPa
T₁ = 27°C
D₁ = 10 m
v₂ = 1.2 × v₁
p ∝ α·D
α = Constant
v₂ = 1.2 × v₁ = 1.2 × 523.6 = 628.32 m³
Therefore, D₂ = 10.63 m
We check the following relation for a polytropic process;
We have;
n = -1/3
Therefore, the relation, pVⁿ = Constant
b. The temperature T₂ is found as follows;
T₂ = 300.15/0.784 = 382.75 K = 109.6°C
c.
p₂ = 100000/0.941 = 106.265 kPa
The work done by the balloon boundaries = 10.81 MJ
Work done against atmospheric pressure, Pₐ, is given by the relation;
Pₐ × (V₂ - V₁) = 1.01×10⁵×(628.32 - 523.6) = 10576695.3 J
The work done on the surrounding atmospheric air = 10.6 MJ