Respuesta :
Answer:
[tex]P_A = 1.25P_B[/tex]
This shows that at a constant net force on the sealed container, the molecular collisions of the ideal gas on side A is greater than the molecular collisions of the ideal gas on side B by a factor of 1.25.
Explanation:
Area of side A = 80cm²
Area of side B = 100cm²
Pressure exerted by the ideal gas is given as force per unit area
[tex]Pressure = \frac{Force}{Area} \\\\Force = Pressure \ * \ Area\\\\F = PA\\\\at \ constant \ net \ force,( F) \\\\P_1A_1 = P_2A_2\\\\P_AA_A = P_BA_B\\\\\frac{P_A}{P_B} = \frac{A_B}{A_A} \\\\\frac{P_A}{P_B} = \frac{100}{80}\\\\\frac{P_A}{P_B} =1.25\\\\P_A = 1.25P_B[/tex]
Thus, the pressure exerted on side A is 1.25 times the pressure exerted on side B.
This shows that at a constant net force on the sealed container, the molecular collisions of the ideal gas on side A is greater than the molecular collisions of the ideal gas on side B by a factor of 1.25.
An ideal gas is a hypothetical gas based on theory
- The expression that correctly compares pressure P exerted on sides A and B of the container is [tex]P_A = P_B[/tex]
- However, the net force on side A, [tex]F_A[/tex], is lesser than the force acting on side B, [tex]F_B[/tex]
The reason the above equations are correct are as follows:
Given:
The type of container in which the ideal gas is sealed = Rectangular container
The area of side A of the container = 80 cm²
The area of side B of the container = 100 cm²
Required:
To give an expression that correctly compares the pressure P exerted on sides A and B of the container and explains the relationship in terms of net force and molecular collisions with the sides
Solution:
For an ideal gas, the pressure exerted on the walls of the container is given by the formula;
P·V = 1/3·N·m·[tex]\overline v^2[/tex]
Where;
P = Pressure
V = The volume of the container
N = Number of molecules
m = The mass of one molecule
[tex]\overline v^[/tex] = Average molecular speed
Therefore, given that average molecular speed is the same for all molecules, the pressure is equal on all the walls of the container
However, Pressure = Force/Area
Therefore, for Force/Area to be the same, the force exerted on the side with a larger area (side B) is larger than the force exerted on a smaller area
Which gives;
[tex]P_A = P_B[/tex] The pressure is the same on both sides because although the average force exerted by the individual molecules as they collide with the sides is the same, the net force and area are both proportionally greater for side B
[tex]P_A = P_B[/tex], [tex]F_A < F_B[/tex]
Learn more about the ideal gas properties here:
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