Question

Keeping the temperature as constant, if a gas in a container is compressed four times of its initial pressure. The volume of gas changing from 20cc(v1cc) to v2cc. Find the final volume v2

Answer 1

• The Final Volume = $\sf{5\:cm³}$

Explanation:

Before solving the problem, let's get to know about Boyle's Law as this problem is based on Boyle's Law.

Boyle's Law :-

When the temperature of a gas is kept constant, the volume of a fixed mass of gas is inversely proportional to its pressure.

P ∝ 1 / V, where PV = constant.

Given :

• Initial Pressure $\sf{P_1\:=\:P}$
• Final Pressure $\sf{P_2\:=\:4\:×\:P\:=\:4P}$
• Initial Volume $\sf{V_1\:=\:20cc\:=\:20cm³}$

To find :

• Final Volume $\sf{F_2\:=\:?}$

According to the question :

By Boyle's Law,

PV = Constant

$⟹\sf{P_1V_1\:=\:P_2V_2}$

$⟹\sf{V_2\:=\:{\dfrac{P_1V_1}{P_2}}}$

$⟹\sf{V_2\:=\:{\dfrac{P\:×\:20\:cm³}{4P}}}$

$⟹\sf{V_2\:=\:5\:cm³}$

• Hence, The Final Volume = $\sf{V_2\:=\:5\:cm³}$