Question

A cylinder of 20 litres capacity contains a gas at 100
atmospheric pressure. How many flasks of 200 cm
capacity can be filled from it at 1 atmosphere pressure,
temperature remaining constant ? [Ans. 10,000 flasks]​

Answer 1

Solution:

As per the given data,

• P₁ = 100 atm
• V₁ = 20 L
• P₂ = 1 atm

Step I: Find V₂

As per the ideal gas equation,

$\dag\boxed{\sf{PV =nRT}}$

here,

• P = pressure
• V = volume
• n = moles
• R = universal gas constant
• T = temperature

All the terms on the R.H.S are constant.

⇒ PV = constant

From this, we can conclude that,

P ∝ 1 / V

Boyle's Law

This law states that the pressure of an ideal gas is inversely proportional to its volume at a constant temperature.

Hence,

⇒ P₁ V₁ = P₂ V₂

⇒ V₂ = P₁ x V₁ / P₂

⇒ V₂ = 100 x 20 / 1

⇒ V₂ = 2000 L

Volume of one flask = 200 cm³ = 200 x 10⁻³ L

Total no of flasks required to occupy a volume of 2000 L

=  2000 / 200 x 10⁻³

= 10,000

The total number of flasks is 10,000.

Answer 2

Question:

A cylinder of 20 litres capacity contains a gas at 100 atmospheric pressure. How many flasks of 200 cm³ capacity can be filled from it at 1 atmosphere pressure, temperature remaining constant?

Answer:

Given:

V1=20L=20000cm³

P1=100atm

V2=?

P2=1

According to Boyles' Law,

P1V1=P2V2

Solution:

100 × 20000 = 1 × V2

2000000 = V2

Also asked that,

how many flasks of 200 cm³ capacity can be filled from it at 1 atmospheric pressure and temperature remain constant.

Therefore,

According to Question:

2000000cm³ ÷ 200cm³

=10000 flasks Ans

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