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?

Answer 1

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 = 1.4

For an adiabatic process, we have:

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

∴

Hence, the pressure increases by a factor of 2.639.