MOaD 7

Question 1

how can Adiabatic conditions be achieved

Answer 1

Adiabatic conditions can be achieved by thermally insulating the system such that now expanding a gas will lower its temperature while compressing it will raise its temperature.

Question 2

does p align with boyles law?

Answer 2

pfalls off faster with V than Boyle’s Law predicts, following a curve like (p ∝ 1/V γ),

Question 3

what is γ

Answer 3

γ = Cp / CV.

Question 4

boyles law formula relating to γ

Answer 4

piVi γ =pfVf γ , orpV γ =constant

Question 5

Show that for a monatomic gas γ = 5/3, and for a non-linear molecule at 298 K, γ = 4/3.

Question 7

calculate the final temperature, Tf, following an adiabatic expansion.

Answer 7

𝑇_f=𝑇_i (𝑉_i/𝑉_f )^(1⁄𝑐)

Question 8

c value formula

Answer 8

c = CV,m / R

Question 9

population levels and adiabatic conditions

Answer 9

In reversible, adiabatic expansion, the population of energy levels does not change but the levels themselves get closer together – this implies a lowering of temperature.

Question 10

What is the final pressure and temperature when 1 mol of argon (assume it’s a perfect gas) is expanded adiabatically and reversibly to twice its original volume, from a starting temperature of 298 K and pressure 1 atm?

Answer 10

For a monatomic perfect gas: CV,m = (3/2)R, so γ = 5/3, c = 3/2.

    pf = pi (Vi / Vf)γ     =    1 × (1/2)5/3       =    0.315 atm

    Tf = Ti (Vi / Vf)1/c   =    298 × (1/2)2/3    =    188 K

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