# Thermodynamics: Heat and Work in a Cylinder

1. Sep 7, 2015

### Sirsh

1. The problem statement, all variables and given/known data

2. Relevant equations
W = ∫pdV
W = (1/2)*k*(x2212)
F = p*A
3. The attempt at a solution

1. Quasistatic process.
2. Pressure is constant.

Force balance on the piston reveals
-> = <-
p0*Apiston = patm*Apiston hence p0 = patm = 101 kPa

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

W12 = p0*Apiston*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*Apiston*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:

Wtotal = W12 + W23(const) + W23 (spring)
Wtotal = 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.

2. Sep 7, 2015

Looks good.