Question

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.

Thus, the process is adiabatic

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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