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Concept : Thermodynamics ​

Answer 1

The cylinder is fully isolated from the rest of the environment.

There is no heat exchange between the system (cylinder) and its surroundings as a result of the design. As a result, the process is called adiabatic.

P1 represents the initial pressure inside the cylinder.

P2 is the final pressure within the cylinder.

V1 is the volume of the cylinder at its beginning.

The final volume of the cylinder is equal to V2.

The specific heat ratio, = Cp / Cv = 1.4,

We have the following for an adiabatic process:

P1V1γ = P2V2γ

After compression, the final volume is reduced to half of its original size.

Hence,

V2 = V1 / 2

P1V1γ = P2(V1 / 2)γ

P2 / P1 = V1γ / (V1 / 2)γ

= 21.4

We get,

= 2.639

Therefore, the pressure increases by a factor of 2.639

Step-by-step explanation:

hope it helps you

Answer 2

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?

Solution :

The cylinder is completely insulated from its surroundings. As a result, 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 heats, γ=CVCP=1.4

For an adiabatic process, we have:

P1V1γ=P2V2γ

The final volume is compressed to half of its initial volume.

∴V2=V1/2

P1V1γ=P2(V1/2)γ

P2/P1=V1γ/(V1/2)γ

=21.4=2.639

Hence, the pressure increases by a factor of 2.639.