# Thermodynamic cycle, work, energy heat input solving

1. Jan 7, 2009

### sm1t

1. The problem statement, all variables and given/known data
An ideal diatomic gas, in a cylinder with a moveable piston undergoes the rectangular cyclic process shown below. Assume that the temperature is always such that the translational and rotational degrees of freedom are active but the vibrational modes are "frozen out". Also, assume that the only type of work done on the gas is the quasi-static compression-expansion work.

The diagram show a square process, 1) p1 to p2 at constand v1 2) v1 to v2 at constant p2 3)p2 to p1 at constant v2 4) v2 to v1 at constant p1

For each of the four steps 1) through 4), compute the work done on the gas, the heat added to the gas and the change in the internal energy of the gas. Express all answers in terms of P1, P2, V1 and V2 and suggest how each of the steps in the cycle could be physically achieved.

2. Relevant equations
PV = nRT
U = 1/2 NfkT

3. The attempt at a solution
I'm a bit thrown off by the quasistatic work, for the pressure change parts I would have used W = integral of PdV but quasistatic work means its done over an infinite amount of time, so do I not use that?

2. Jan 7, 2009

### Mapes

I hope you mean "volume change" or "constant-pressure" here! $W=\int P\,dV$ isn't meant for constant-volume, pressure changing processes.

It's typical to assume quasistatic processes; that part is OK.

3. Jan 8, 2009

### Andrew Mason

A quasi-static process is one in which the system is arbitrarily close to equilibrium at all times during the process. Don't worry about it in this problem.

The work done is always $\int PdV$ where P is the external/internal pressure (external and internal pressure will be arbitrarily close since it is a quasi static process). On the PV diagram how is this work shown graphically?

Since P does not change for 2 and 4 and V does not change for 1 and 3, it is pretty easy to determine the work done on the gas. I think that was Mapes' point. Be careful with the sign. When is positive work being done on the gas? When is negative work being done on the gas?

AM