# Closed system piston cylinder device problem

1. Dec 2, 2009

### ricof

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

A closed system comprising a cylinder and frictionless piston contains 1kg of a perfect gas of which molecular mass is 26. The piston is loaded so that the pressure is constant at 200kPa. Heat is supplied causing the gas to expand from 0.5m^3 to 1m^3. Calculate heat supplied

2. Relevant equations

w = int-(PdV)

PV = nRT

q = du - w

3. The attempt at a solution

I have worked out w as 100kJ by doing PdV = 200kPa x 0.5

Oh and Cp = 1.08 kJ/kg/K

Now am stuck.

2. Dec 2, 2009

### Andrew Mason

How did you get this? What is Oh?

You can determine the beginning and ending temperatures of the gas using the ideal gas equation.

Then determine the change in internal energy of the gas: $\Delta U = nC_v\Delta T$. Add that to the work done (which you have found) and that will give you the heat flow.

OR, as this is a process at constant pressure, you can simply use $$Q = nC_p\Delta T$$

Either way, however, you need to know the degrees of freedom of the gas. It is not monatomic as it would have to be iron. So it has either 2 or 3 degrees of freedom.

AM

3. Dec 2, 2009

### ricof

Sorry, 'Oh' as in the figure of speech.

So I use ideal gas law with the same P but different V each time to find the temperatures?

What does degree of freedom mean? I haven't heard of that before.

4. Dec 2, 2009

### Andrew Mason

Correct.

It is part of the kinetic theory of gases. See: http://en.wikipedia.org/wiki/Kinetic_theory

A monatomic gas has 3 degrees of freedom (of translational motion). A diatomic molecule has 5 degrees of freedom (because it can also spin on two perpendicular axes) and a polyatomic molecule has even more degrees of freedom (because it may be able to rotate on 3 axes and may also vibrate in different ways depending on its structure). Energy absorbed by a monatomic gas all goes into translational energy (which directly increases temperature and pressure). Energy absorbed by diatomic and polyatomic gases goes into rotational and vibrational energy, which does not affect temperature or pressure. So the number of degrees of freedom determines the heat capacity of the gas.

AM