Question

The pressure of a gas constant temperature is increased by a factor od 4 by what factor does the volume change

Answer 1

Answer:

$\frac{1}{4}$

Explanation:

From the given problem, we are to find the factor number by which the volume of the compressed gas has changed through.

We apply Boyle's law to this problem because the condition of the reaction stipulates a constant temperature.

Boyle's law states "the volume of a given mass of gas is inversely proportional to its pressure provided that temperature remains constant". Mathematically, it is expressed as:

                           P₁V₁ = P₂V₂

P₁ is initial pressure on the gas

V₁  is the initial volume of the gas

P₂ is the final pressure of the gas

V₂ is the final volume of the gas

From the problem, we are to find the factor through which the volume changed:

             P₁V₁ = P₂V₂

              V₂ = $\frac{P_{1} }{P_{2} } V_{1}$

             

Now:

P₁ =  P₁

P₂ = 4P₁

                V₂ = $\frac{P_{1} }{4P_{1} } V_{1}$

Therefore, the factor of the volume change is $\frac{1}{4}$