Answer:
The length the divider is to equilibrium from Part A = 1.30 m and from Part B = 3.70 m
Explanation:
Given that:
A rectangular cube with 3.2 m breadth, 1.2 m height and 5 m in length is splitted into two parts.
The diagrammatic expression for the above statement can be found in the attached diagram below.
The container has a movable airtight divider that divides its length as necessary.
Part A has 58 moles of gas
Part B has 165 moles of a gas.
Thus, the movable airtight divider will stop at a length where the pressure on it is equal on both sides.
i.e
[tex]\mathtt{P = P_A = P_B}[/tex]
Using the ideal gas equation,
PV = nRT
where, P,R,and T are constant.
Then :
[tex]\mathsf{\dfrac{V_A}{n_A}= \dfrac{V_B}{n_B}}[/tex]
[tex]\mathsf{\dfrac{L_A \times B \times H}{n_A}= \dfrac{L_B \times B \times H}{n_B}}[/tex] --- (1)
since Volume of a cube = L × B × H
From the question; the L = 5m
i,e
[tex]\mathsf{L_A +L_B}[/tex] = 5
[tex]\mathsf{L_A = 5 - L_B}[/tex]
From equation (1) , we divide both sides by (B × H)
Then :
[tex]\mathsf{\dfrac{L_A }{n_A}= \dfrac{L_B }{n_B}}[/tex]
[tex]\mathsf{\dfrac{5-L_B}{58}= \dfrac{L_B }{165}}[/tex]
By cross multiplying; we have:
165 ( 5 - [tex]\mathsf{L_B}[/tex] ) = 58 (
825 - 165[tex]\mathsf{L_B}[/tex] = 58
825 = 165[tex]\mathsf{L_B}[/tex] +58
825 = 223[tex]\mathsf{L_B}[/tex]
[tex]\mathsf{L_B}[/tex] = 825/223
[tex]\mathsf{L_B}[/tex] = 3.70 m
[tex]\mathsf{L_A = 5 - L_B}[/tex]
[tex]\mathsf{L_A = 5 - 3.70}[/tex]
[tex]\mathsf{ L_A}[/tex] = 1.30 m
The length the divider is to equilibrium from Part A = 1.30 m and from Part B = 3.70 m
