Question

At constant temperature, what relative effect would each of the following changes have on the condition specified using P1V1 = P2V2? a. effect on the volume of doubling the pressureb. effect on the pressure of tripling the volumec. effect on the pressure by reducing the volume to one fourth of its original value

Answer 1

Explanations:

Given the formula for the condition expressed as:

`P_1V_1=P_2V_2`

where:

• P1 and P2 are the ,initial and final pressure ,respectively

,

• V1 and V2 are the, initial and final volume, respectively

a) If the pressure is doubled, then the final pressure P2 will be 2P1

Substituting P2 = 2P1 into the formula, we will have:

`\begin{gathered} \cancel{P_1}V_1=(2\cancel{P_1}_{})V_2 \\ V_1=2V_2 \\ V_2=(1)/(2)V_1 \end{gathered}`

This shows that the volume will be halved if the pressure is doubled.

b) If the volume is tripled, this means that V2 = 3V1. Substituting the volume will give:

`\begin{gathered} P_1_{}_{}\cancel{V_1}=P_2(3\cancel{V_1}_{})_{} \\ P_1=3P_2 \\ P_2=(1)/(3)P_1 \end{gathered}`

Hence if the final pressure will be one-third of the initial if the volume is tripled.

c) If the volume is reduced to one-fourth of its original value, then the new volume will be given as:

`V_2=(1)/(4)V_1`

Substituting this into the formula:

`\begin{gathered} P_1\cancel{V_1}_{}=P_2((1)/(4)\cancel{V_1}) \\ P_1=(1)/(4)P_2 \\ P_2=4P_1 \end{gathered}`

This shows that if the volume is reduced to one-fourth of its original value, the pressure will be quadrupled