What happens to the volume of a gas if the pressure decreases by 5 %?

2 Answers
diwa · Ernest Z. · Al E.
Feb 17, 2018

5 % increase.

Explanation:

Use

#PV = nRT#

  • For first case, #color(white)(m)PV = nRTcolor(white)(m)bb((1)#
  • For second case, #pv=nRTcolor(white)(m)bb((2))#

Per (1) and (2),

#pv = PV#

#v=(PV)/p = (PV)/(0.95P) = (100V)/95 = 1.05V# (105 % of original volume)

#"Increase in"color(white)(l) V = "105 % - 100 % = 5 %"#.

Al E.
Feb 17, 2018

Consider,

#PV = nRT#

#=> P_1V_1 = nRT = P_2V_2#

#therefore P_1V_1 = P_2V_2#

Moreover, consider in the first case that #P = 1#, and in the second case #P = 1 - 0.05 = 0.95#.

Hence,

#PV_1 = 0.95PV_2#

#=> 1.05V_1 = V_2#

To be sure, if the pressure is decreased by #5%#, ceteris paribus, then the volume will increase by approximately #5%#. This is dictated by the inverse relationship mathematically illustrated above.

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