The initial pressure in the cylinder of 10 bar of argon with = (5/2)·R
and the added gas at pressure of 50 bar gives the following values.
(a) 400.6 K
(b) 51.184 J
(c) The pressure of the cylinder when it is shipped is 37.194 bar
<h3>How can the temperature, heat transferred and pressure be calculated?</h3>
(a) Adiabatic compression, we have;
Where;
Therefore;
Which gives;
The temperature
Using an ideal gas model, we have;
Which gives;
V₁ = 2.625·V₂
Volume occupied by the gas in the cylinder after the pressure increases is therefore;
Volume of gas added is therefore;
Considering a molar volume of gas, we have;
0.040 × 0.619 × 2.5×8.3145×(T₃ - 298) = 0.040 × 0.381 × 2.5×8.3145×(567.29 - T₃)
Solving gives;
T₃ ≈ 400.6 K
For a molar volume of gas cylinder, the temperature just after the valve is closed is T₃ ≈<u> 400.6 K</u>
(b) If the cylinder sits in the storage for a long time, and heat is conducted out, we have;
The temperature of the cylinder will revert to room temperature of 298 K
The heat transferred is therefore;
0.040 × (2.5 × 8.3145 - 8.3145) ×(400.6 - 298) ≈ 51.184
The heat transferred from the cylinder is 51.184 J
(c) The pressure of the gas in the cylinder is therefore;
Which gives;
Therefore;
The pressure of the cylinder when it is shipped is 37.194 bar
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