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A conducting and closed container of capacity 100 liter contains an ideal gas at a high pressure. Now using a pump, the gas is taken out at a constant rate of 5 liter/sec. Find the time taken in which the pressure will decrease to initial (P_("initial"))/(100) ? (Assume isothermal condition) |
Answer» Solution : The gas is taken out at the rate of 5 lit/sec. The volume of gas ejected in 'DT' time is (vol) = 5 dt Moles of gas ejected `=(n)/(v)(5dt)` `PV=nRT""rArr""(dp)V=(dn)RT""rArr""(dp)V=-((n)/(V)5dt)RT` `rArr""(dp)V=-5dt(nRT)/(V)=-(5dt)P` `rArr""(dp)/(p)=(5)/(V)dt""rArr""(dp)/(p)=-(5)/(100)dt=-(1)/(20)dt` `int_(p=p_(i))^(p=p_(f))(dp)/(p)=-(1)/(20)int_(t=0)^(t=t)dt""rArr""p_(f)=p_(i)E^(-(1)/(20))""rArr""(p_(i))/(100)=p_(i)e^(-(1)/(20))` T= 20 ln 100 `=20xx2ln 10=92 sec.` |
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