Question

A cylinder with a movable piston contains 0.25 mole of monatomic idea gas at 2.40×10⁵,Pa and 355 K. The ideal gas first expands isobarically to twice its original volume. It is then compressed adiabatically back to its original volume, and finally it is cooled isochorically to its original pressure. Compute the temperature after the adiabatic compression.

Answer 1

The final pressure after the adiabatic compression is 7.20 x 10^5 Pa.

Step-by-step explanation:

The adiabatic compression of a gas can be analyzed using the adiabatic equation:

P₁V₁^γ = P₂V₂^γ

Where P₁ and V₁ are the initial pressure and volume, P₂ and V₂ are the final pressure and volume, and γ is the heat capacity ratio for the gas.

In this case, the gas is compressed adiabatically back to its original volume, so V₂ = V₁. We can rearrange the equation to solve for P₂:

P₂ = P₁(V₁/V₂)^γ

Substituting the known values, we get:

P₂ = 2.40 x 10^5 Pa((2)(5 x 10^-2 m³)/5 x 10^-2 m³)^(5/3)

Calculating the result, we find that the final pressure after the adiabatic compression is 7.20 x 10^5 Pa.