Question 12 A cylinder has a piston at one end that can be moved in or out to ch

Question

Question 12

A cylinder has a piston at one end that can be moved in or out to change the volume of gas inside. The other end is fitted with a valve. Initially the cylinder contains 4.05 mol of an ideal gas. The piston is now pushed in to decrease the volume of gas to three-fifths its initial value without causing any change in temperature. In order to keep the pressure constant as well, how many moles of gas need to be released through the valve?

___________moles

please show step by step solving with the appropriate formulas, thank you :)

Explanation / Answer

Here , T is constant i.e. T1 = T2 , so , (P1*V1) / n1 = (P2*V2)/n2 ,

here , pressure should be constant , so V1/n1 = V2/n2 , given V2 = 3/5 (V1) , so we get V1/ V2 = n1 / n2 ,

n1 / n2 = 5/3 , but n1 = 4.05 moles , so n2 = 4.05 (3/5) = 2.43 moles

so , no.of moles of gas to be removed is (4.05-2.43) moles = 1.62 moles.

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