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A cylinder with a movable piston contain...

A cylinder with a movable piston contains3moles of hydrogen atstandard temperature and pressure. The walls of the cylinder are made of a heat insulator, and the piston is insulated by having a pile of sand on it. By what factor does the pressure of the gas increase if the gas is compressed to half its original volume ?

Text Solution

Verified by Experts

We are given:
Initial volume, `V_(1) = V`
  Final volume, `V_(2) = (V)/(2)`
We know that compression of gas is an adiabatic process.
Also, Hydrogen is a diatomic gas therefore, the ratio of two specific heat is
`gamma = (7)/(5) = 1.4`
`P_(1)V_(1)^(gamma)`, we get `(P_(2))/(P_(1)) = ((V_(1))/(V_(2)))^(gamma)`
Or, `(P_(2))/(P_(1)) = [(V)/(V//2)]^(1.4) = (2)^(1.4) = 2.64`
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