Question

Two cylinders X and Y filled with oxygen are connected to teach other with a tub, The tube is closed with a tap. The pressure in X is 800 mm and that in Y is 400 mm. If the connecting tube is opened, what will be the resulting pressure in the cylinders?
give step by step explanation
pls answer fast.

Answer 1

Explanation:

Two cylinders X and Y filled with oxygen are connected to teach other with a tub, The tube is closed with a tap. The pressure in X is 800 mm and that in Y is 400 mm. If the connecting tube is opened, what will be the resulting pressure in the cylinders?

give step by step explanation

pls answer fast.

1200 mm

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Answer 2

After opening the connecting tube the resulting pressure in the cylinders would be 600 mm.

Given:

Pressure in Cylinder X (P₁)= 800 mm

Pressure in Cylinder Y (P₂) = 400 mm

Volume of Cylinder X (V₁) = Volume of Cylinder Y (V₂) = V

To Find:

Resulting Pressure in the cylinders

Solution:

Let the volumes of both cylinders 'X' and 'Y' be equal to 'V'

We can solve the given question by using Boyle's Law.

• Boyle's law states that at a constant temperature the Pressure is inversely proportional to Volume.

• $i.e. P = \frac{K(constant)}{V}\\\\\\Hence:PV = constant$

• Therefore by Boyle's law we may say that at a constant temperature the product of Pressure and Volume of the containers remain constant.
• So we conclude that at constant temperature: PV = constant and for two cylinders we can say that: P₁V₁ + P₂V₂ = P₃V₃, where 'P₃' and 'V₃' are the final pressure and volume of the combination of cylinder.
• As given in the question, after opening the connecting tube the final volume of the cylinders would be equal to V₃ = V₁ + V₂ = V + V = 2V

Therefore: P₁V₁ + P₂V₂ = P₃V₃

∴ 800 × V + 400V = P₃ × (2V)

→1200V = 2P₃V

→2P₃ = 1200

∴ P₃ = 600 mm

Hence, after opening the connecting tube the resulting pressure in the cylinders would be 600 mm.

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