Question

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?
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Answer 1

Answer:

Explanation:

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 y , = 1.4

For an adiabatic process, we have:

P1V1^Y=P2V2^Y

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

∴V2=V1/2

P1V1^Y=P2(V1/2)^Y

P2/P1=V1^Y/(V1/2)^Y

=2^Y=2^1.4=2.639

Hence, the pressure increases by a factor of 2.639.

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