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# An ideal gas is enclosed in a container of volume V at a pressure P. It is being pumped out of the container by using a pump with stroke volume v. What is final pressure in container after n-stroke of the pump?— (1) P(V/V+v)^n, (2) PV/(V-v)^n, (3) PV^n/v^n, (4) P(V/V-v)^n

Asked by patra04011965 20th June 2019, 3:39 PM
Let us assume m number of moles of ideal gas present in the container of volume V initially

at temperature T and pressure P.

we have,  P V = m R T  .............................(1)

During first stroke, volume v is pumped out . Number of moles left out in container  =  m(V-v)/V.

after the first stroke, pressure decrases to P1 , volume of gas in the container remains constant.
Also we assume this is isothermal process

hence now we have,   P1 V = [ m(V-v)/V ] R T ..................(2)

By dividing eqn.(2) by eqn.(1), we get, ( P1 / P ) = (V-v)/V = [ 1 - (v/V) ]

Hence after first stroke, pressure P1 = P [ 1 - (v/V) ] .............................(3)

In same manner, we get the pressure P2 after second stroke as,  P2 = P1[ 1 - (v/V) ] .....................(4)

using eqn.(3), we rewrite eqn.(4) as,  P2 = P [ 1 - (v/V) ]2

After n stroke,  pressure in the container,   Pn = P [ 1 - (v/V) ]n = P [ (V-v)/V ]n

Answered by Expert 20th June 2019, 4:59 PM
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Tags: pressure