Question

3. Let the pressure P and volume V for a certain gas. If the pressure is increased by 25% at a constant temperature, then what would be the volume of the gas?

0.6V
0.75V
0.8V
0.85V​

Answer 1

Explanation:

PV=nRT

PV=constant

P×V=P'×V'

P×V=1.25P×V'

V'=V/1.25

V'=0.8V

Answer 2

Answer:

Option 3rd is correct. 0.8V.

Explanation:

To find :

• Volume of the gas means V₂.

Assume, P₁ and P₂ be Initial and final pressure respectively. And, V₁ and V₂ be Initial and final volume of gas respectively.

Given,

Pressure is P and Volume is V.

• P₁ = P.
• V₁ = V.

Pressure is increased by 25%.

→ P₂ = P + 25% of P.

→ P₂ = P + 25P/100

→ P₂ = P + P/4

→ P₂ = (4P + P)/4

→ P₂ = 5P/4

Here,

Temperature is constant.

We know,

Boyle's law :

✿ P₁V₁ = P₂V₂ [It is relation between the Pressure and the Volume at constant temperature ]

Now, Put all values :

$\implies \sf P \times V = \dfrac{5 P}{4} \times V_{2}$

$\implies \sf P \times V \times \dfrac{4}{5 P} = V_{2}$

$\implies \sf \cancel{P} \times V \times \dfrac{4}{5} \times \dfrac{1}{\cancel{P}} = V_{2}$

$\implies \sf V \times 0.8 = V_{2}$

$\implies \pmb{ \sf V_{2} = 0.8 V}$

Therefore,

Volume of the gas is 0.8V.