Question #961df

2 Answers
anor277
Feb 25, 2016

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#.

Dr. Hayek
Feb 25, 2016

#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.

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