Thermodynamics: Heat and Work in a Cylinder

[Sirsh]

Homework Statement

Homework Equations

W = ∫pdV
W = (1/2)*k*(x₂²₁²)
F = p*A

The Attempt at a Solution

Assumptions made:
1. Quasistatic process.
2. Pressure is constant.

Force balance on the piston reveals
-> = <-
p₀*A_piston = p_atm*A_piston hence p₀ = p_atm = 101 kPa

From states 1-2 this is a constant pressure process:

W₁₂ = p₀*A_piston*d1 = (101 kPa)(44*10^-4 m²)(0.075m) = 33.333 Joules

From states 2-3 this is both a constant pressure process and a spring compression process (taken separately):

W23 (const) = p₀*A_piston*d2 = (101 kPa)(44*10^-4 m²)(0.075m) = 33.333 Joules

W23 (spring) = (1/2)*k*(x₂²₁²) = (1/2)*(9800 N/m)(0.075m)² = 27.562 Joules

Total work done from the initial to the final state is equal to the summation of the three works done above:

W_total = W₁₂ + W₂₃(const) + W2₃ (spring)
W_total = 33.333 + 33.333 + 27.562 = 94.228 Joules of work done.

Is my approach to this question reasonable? If not what can I do to fix or look up where I've gone wrong?

As always, every ones help is greatly appreciated.

 

[Chestermiller]

Looks good.