Question

A gas is expanded, at constant temperature, from a volume of 400 ml to a volume of 1 litre, where its final pressure is 100 mm of Hg. What was the original pressure?

Answer 1

From the given,

Volume, $({ V }_{ 1 })$ = 400 ml  

$({ V }_{ 2 })$ = 1 L = 1000 ml

Pressure, $({ P }_{ 1 })$ = ?

$({ P }_{ 2 })$ = 100 mm of Hg temperature is constant

According to the Boyle's law,

${ P }_{ 1 }{ V }_{ 1 }\quad =\quad { P }_{ 2 }{ V }_{ 2 }\quad$

Substitute the given values,

${ P }_{ 1 }\quad =\frac { { P }_{ 2 }{ \quad \times \quad V }_{ 2 } }{ { V }_{ 1 } } \\ \\\quad \quad =\quad \frac { 100\quad \times \quad 1000 }{ 400 } \quad =\quad 250\quad mm\quad of\quad Hg$

Therefore, original pressure is 250 mm of Hg

Answer 2

Given :-

• A gas is expanded, at constant temperature from a volume of 400 ml to a volume of 1 litre. The final pressure of the gas is 100 mm of Hg.

To Find :-

• What is the initial pressure of the gas in mm ?

Solution :-

Given,

• A gas is expanded, at constant temperature from a volume of 400 ml to a volume of 1 litre.
• The final pressure of the gas is 100 mm of Hg.

We know that,

• $\sf V _{1}$=400
• $\sf V_{2}$=1000 (1 lit)
• $\sf P_{2}$=100

According to the Boyle's law,

$\sf\implies \: P_{1}V_{1} = P_{2}V_{2}$

$\sf\implies \: P_{1} \times 400 = 100 \times 1000$

$\sf\implies \: P_{1} \times 400 = 100000$

$\displaystyle\sf\implies \: P_{1} = \frac{100000}{400}$

$\displaystyle\bf\implies \: P_{1} = 250$

Hence,

∴ The initial pressure of the gas is 250mm .

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