# Homework Help: Adiabatic thermo problem

1. Jul 8, 2014

### le@rner

1) If in a system(consider a cylinder) fixed with a piston , if the piston is moved suddenly then how can a process be adiabatic.
2) I understood that the process would be irreversible but, if the process is adiabatic then is the relation PV^y = constant (where y is gamma, P is pressure, V is volume) is true for irreversible process too. (In many books they have written that the relation is true only for reversible processes)

In the following question , I am not getting the real essence of the mechanics of the process. Please explain:

Question:
A gas is enclosed in a cylindrical can fitted with a piston. The walls of the can are adiabatic. The initial pressure, volume and temperature of the gas are 100 kPa, 400 cc (cubic cm) and 300 K respectively. The ratio of the specific heat capacities of the gas is Cp/Cv=1.5 . Find the pressure and temperature of the gas if it is (a)suddenly compressed to 100 cc (cubic cm). (b)slowly compressed to 100 cc (cubic cm).

Here, the answer to both the cases is given same by taking PV^y = constant (where y is gamma)

2. Jul 8, 2014

### Ry122

one is constant entropy due to no dissipation in energy. The other isnt so you need to use tables to find the loss due to entropy.

there's no entropy for systems where there's an infinite number of small changes.

3. Jul 8, 2014

### Staff: Mentor

Adiabatic means that no heat enters or leaves the system. If the cylinder is ideally insulated, then no heat will enter or leave the system, irrespective of the nature of the deformation.
The books you have are correct. The relation is true only for reversible adiabatic processes.
As I said, the relation is only applicable to reversible adiabatic expansion and compression. This is not the case if the gas is suddenly compressed by a factor of 4. The case of a "sudden" compression cannot be done unless more information is available. An example of the type of additional information that would be required would be specifying that the external force per unit area on the piston is constant, and of appropriate magnitude for the final volume to be 100 cc. This would give a very rapid compression. The rapid compression is going to involve irreversible viscous dissipation of mechanical energy, and cannot be described by the reversible deformation relationship. However, this problem can be solved.

Chet