Question

A monatomic ideal gas is contanined in a cylinder with a moveable piston. Initially the volume of the cylinder is 0.25m^3. The gas is compressed under a constant pressure of 3 Pa until the volume has been halved. Then the volume is held constant while the pressure is doubled. Finally, the gas is allowed to expand isothermally back to its original condition.

a)Sketch a P-V diagram for this process. Label the corners 1, 2, 3 with 1 being the beginning point.

b) If the temperature was 27 degrees at the beginning, what was the temperature at the end of the isobaric process?

c) how many moles of gas are there? How many particles of gas are there?

d) what is the total thermal energy of the system at the beginning of the process?

e) Find the work, heat and change in thermal energy for each step of the process. Place your final answers in a chart.

I got part b by using Tfinal=Tinitial*(Vfinal/Vinital)= 150K but am not getting the correct answers for the rest part c I know I use n=pV/RT but for some reason not coming up with the correct answer. Please Help???

Answer 1

Given V₁= 0.25 m³ , P₁ = 3 Pa , T₁ = unknown

           V₂ = 0.125 m³ , P₂ = 3 Pa , T₂ = unknown

           V₃ = 0.125 m³ , P₃ = 6 Pa , T₃ = T₁

part a

Applying ideal gas equation at 1 and 2

P1V1/P2V2 = T1/T2   => 0.25*3/(0.125*3) = T1/T2 => T₂ = T₁ / 2

Part b

At the end of isobaric process, temperature is T₂ = T₁/2 = 27/2 = 13.5⁰ C = 273+13.5 K = 286.5 K

Part C

Let moles of gas be n

Then n = P1V1/(RT1) = 0.25*3/(8.314*300) = 3*10^-4

No of atoms of gas = n*Avogadro No.

                              = 3*10^-4 * 6.022*10²³

                              = 1.81*10²⁰