Question

What will be the minimum pressure required to compress 500 dm3 of air at 1 bar to 200 dm3 at 30°C?​

Answer 1

$\bigstar$ Answer $\bigstar$

$\checkmark$ To Find:

What will be the minimum pressure required to compress 500 dm³ of air at 1 bar to 200 dm³ at 30°C

$\checkmark$ Solution:

We know that,

$\star$ Boyle's Law

At constant temperature the pressure of a given mass of an ideal gas is inversely proportional to its volume

Mathematically,

$\blue{\rm \implies P \propto \dfrac{1}{V}}$

Therefore,

$\red{\boxed{\rm P_{1}V_{1}=P_{2}V_{2}}}$

Given that,

According to the Question,

We are asked to find the the minimum pressure required to compress 500 dm³ of air at 1 bar to 200 dm³ at 30°C.

Since, the given condition is at constant temperature.

So,

Let us Consider that P₂ is the minimum pressure that is required to compress the gas.

Therefore,

We are asked to find the value of P₂

Hence,

$\orange{\implies \rm P_{2}=\dfrac{P_{1}V_{1}}{V_{2}} }$

Given that,

Volume of the gas ( V₁ ) = 500 dm³

Pressure of the gas ( P₁ ) = 1 bar

Volume of the gas ( V₂ ) = 200 dm³

Therefore,

By Substituting the above values,

We get,

$\green{\implies \rm P_{2}=\dfrac{1 \times 500}{200} \ bar}$

$\blue{\implies \rm P_{2}=\dfrac{500}{200} \ bar}$

$\pink{\implies \rm P_{2}=2.5 \ bar}$

Hence,

Minimum Pressure = 2.5 bar

Answer 2

${ \bf{ \underline{ \red{ \underline{ \red{Question}}}} : - }}$

• What will be the minimum pressure required to compress 500 dm³ of air at 1 bar to 200 dm³ at 30°C?

${ \bf{ \underline{ \red{ \underline{ \red{Solution}}}} : - }}$

• To find :- Minimum pressure required to compress 500 dm³ of air at 1 bar to 200 dm³ at 30°C?

Now,

According to Boyle's Law

{ Boyle's Law :- a law stating that the pressure of a given mass of an ideal gas is inversely proportional to its volume at a constant temperature.}

${ \huge{ \sf{ \dashrightarrow{ \purple{P \: \: \alpha \: \: \frac{1}{V} }}}}}$

According to this

Equation of Boyle's Law

${ \sf{ \dashrightarrow{ \purple{P_{1}V_{1 }= P_{2}V_{2 }}}}}$

where,

${ \sf{ \purple{{\blue{Pressure \: of \: gas \: }} (P_{1} ) = 1 bar }}}$

${ \sf{ \purple{{\blue{Volume \: of \: gas \: }}(V_{1} ) = 500 \: dm³ }}}$

${ \sf{ \purple{{\blue{Volume \: of \: compressed \: gas \: }} (V_{2} ) = 200 \: dm³ }}}$

${ \sf{ \blue{Now\: let \: { \purple{P_{2} }} \: be \: the \: pressure \: required }}}$

${ \sf{ \blue{to \: compress \: the \: gas.}}}$

Accoeding to Boyle's Law

${ \sf{ \dashrightarrow{ \purple{P_{1}V_{1 }= P_{2}V_{2 }}}}}$

${ \sf{ \dashrightarrow{ \purple{1 \times 500= P_{2} \times200}}} }$

${ \sf{ \dashrightarrow{ \purple{500= P_{2} \times200}}} \: \: \: \: \: \: i.e.}$

${ \sf{ \dashrightarrow{ \purple{P_{2} \times200 = 500}}}}$

${ \sf{ \dashrightarrow{ \purple{P_{2} = { \cancel{\frac{500}{200} }}}}}}$

${ \sf{ \dashrightarrow{ \purple{P_{2} = 2.5 \: bar }}}}$

Hence, 2.5 bar is the required pressure to compress the gas.

i hope it helps you.