# Homework Help: Thermodynamics Work, Heat, First Law Question

1. Sep 13, 2010

### Honger

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

Consider two pistons of equal cross sectional area joined as illustrated in the
following sketch (my rendition):
[A|----|B]
• Each piston contains n moles of an ideal gas of specific heat cV=(3/2) R.
• Each piston's base is fixed, so when the rod joining the piston moves one
must expand for the other to compress.
• Piston A is thermally isolated and is initially at a pressure PA0 and a
temperature T0.
• Piston B is held in thermal equilibrium with a bath at temperature T0 and
is initially at pressure PB0, which is higher than the initial pressure in
piston A.
• Piston B is allowed to expand quasi‐statically (reversibly) until there is no
more net force on the rod joining the pistons. Piston B is frictionless, so
during the expansion Pex=PB.
A. Derive an expression that relates the following dimensionless
quantities:
π =P0B/P0A ,τ =TfA/T0A

2. Relevant equations

Ideal Gas: PVm=RT, dW=-PdV=CvdT

3. The attempt at a solution

Since the pistons are connected, when the piston stops moving, the work done in A will be equal to the work done by B?