In: Physics

# By what factor does the pressure of the gas increase if the gas is compressed to half its original volume?

A cylinder with a movable piston contains 3 moles of hydrogen at standard 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?

## Solutions

##### Expert Solution

The cylinder is completely insulated from its surroundings.

Therefore, no heat is exchanged between the system (cylinder) and its surroundings.

Initial pressure inside the cylinder = P1

Final pressure inside the cylinder = P2

Initial volume inside the cylinder = V1

Final volume inside the cylinder = V2

Ratio of specific heat, Y = Cp / Cv = 1.4

For an adiabatic process, we have:

P1V1Y = P2V2Y

The final volume is compressed to half of its initial volume

Hence,

V2 = V1 / 2

P1V1Y = P2(V/ 2)Y

P2 / P1 = V1Y / (V1 / 2)Y

= 21.4

We get,

= 2.639

Therefore, the pressure increases by a factor of 2.639

The pressure increases by a factor of 2.639.

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