# Closed system piston cylinder device problem

• ricof
In summary, a closed system containing 1kg of a perfect gas with a molecular mass of 26 is at a constant pressure of 200kPa. After heat is supplied, the gas expands from 0.5m^3 to 1m^3. To calculate the heat supplied, you can use the ideal gas equation or the change in internal energy equation, taking into account the degrees of freedom of the gas. A monatomic gas has 3 degrees of freedom, a diatomic molecule has 5, and a polyatomic molecule has even more. This determines the heat capacity of the gas.
ricof

## Homework Statement

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

w = int-(PdV)

PV = nRT

q = du - w

## 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.

ricof said:
Oh and Cp = 1.08 kJ/kg/K
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

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.

ricof said:
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?
Correct.

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

## 1. What is a closed system piston cylinder device?

A closed system piston cylinder device is a mechanical system consisting of a cylinder with a movable piston that creates a closed space. This space is filled with gas or liquid that can be compressed or expanded by the movement of the piston.

## 2. How does a closed system piston cylinder device work?

The closed system piston cylinder device works by manipulating the pressure and volume of the gas or liquid inside the cylinder. When the piston moves, it either compresses or expands the gas or liquid, altering its pressure and volume. This change in pressure and volume can be used to do work or generate energy.

## 3. What are the applications of a closed system piston cylinder device?

Closed system piston cylinder devices have a wide range of applications in various industries. They are commonly used in engines, pumps, compressors, and refrigeration systems. They are also used in laboratories and experiments to study the behavior of gases and liquids under different conditions.

## 4. What are the limitations of a closed system piston cylinder device?

One of the main limitations of a closed system piston cylinder device is that it can only work with gases or liquids. It cannot be used with solids. Additionally, the accuracy and efficiency of the device may be affected by factors such as friction, leaks, and temperature changes.

## 5. How is the efficiency of a closed system piston cylinder device measured?

The efficiency of a closed system piston cylinder device is measured by calculating the work output divided by the energy input. This is known as the thermal efficiency and is expressed as a percentage. The higher the thermal efficiency, the more efficient the device is in converting energy into work.

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