Question

Question #961df

Answer 1

Boyle's law holds that for a given quantiy of gas, `P` `prop` `1/V`, or `PxxV=k`; so if the pressure is doubled the the volume is halved, and vice versa.

Explanation:

Given that `P` and `V` are inversely proportional, if the pressure doubled, the volume should reasonably be HALVED; i.e. `PV=k`. Think of a piston (which could be as simple as a syringe). If we depress the piston (reducing the volume), the pressure increases proportionally.

So, for a given quantity of gas at constant temperature, `P_1V_1 =P_2V_2`.

Answer 2

`P_2=2xxP_1=>V_2=(V_1)/2`

Explanation:

Boyle's law states: At constant temperature, and for the same gas in a container, `PV=k`.

Therefore, `P_1V_1=P_2V_2`.

Since the pressure is doubled, thus `P_2=2xxP_1`

`=>P_1V_1=P_2V_2=>cancel(P_1)V_1=(2xxcancel(P_1))V_2`.

`=>V_2=(V_1)/2`

Therefore, according to Boyle's law, when the pressure is doubled, the volume is halved.