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Question
In an isothermal process on an ideal gas, the pressure increases by 0.5%. The volume decreases by about
Options
0.25%
0.5%
0.7%
1%.
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Solution
0.5%
Let p and p' be the initial and final pressures of the system and V and V' be the initial and final volumes of the system. p' is 0.5% more than p and the process is isothernal. So, pV = k = p'V' = constant. Therefore,
pV = p'V'
`=> "p"^"V" = ("P" +0.5/100"p")"V"`
`=> "p"^"V" = 100.5/100"p"^("V'")`
`=> "V'" = 100/100.5"V"`
`=> "V'" -"V" = 100/100.5 "V"-"V"`
` = -0.5 /100.5`
= -0.49 %
So, volume V' decreases by about 0.5% of V.
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