# Thermodynamics : Open and close control systems

• jyotish123
In summary, the expert states that a puncture in a tire will cause a change in the energy balance within the tire and that it will be an adiabatic process.
jyotish123
Hi all,

Q: How do you find out the boundary work using control volume analysis for a tire that is punctured all of a sudden?

To proceed,

I started off by using the tire as a control volume with one outlet.

Using first Law,

E(in) - E(out) = dE/dt

Final Conditions: P(final) = Patm. , T (final) = T(atm)

Can someone help me out with this?

Thanks,
JT

I'm not 100% sure on this, but I think it's not isometric (the tire decreases in volume), it's not isothermal (though it could be depending on the size of the puncture and the tire it takes to relieve the pressure). It's not isobaric since the pressure is changing. So, I would say it's going to be a polytropic or adiabatic process, assuming a somewhat large hole the the tire loses full pressure over the course of a few seconds.

So, rather than going through the energy balance in this case (there's probably a way to use that, it just isn't coming to me at the moment),and since it just asks for boundary work anyway, I would assume adiabatic if they didn't give you a coefficient for the polytropic process. n is some number greater than 1, for air close to room temperature use 1.4 typically. R is the gas constant specific to that gas (not the universal), 287 J/kg K for air.

$$W_{boundary} = \frac{P_2 V_2 - P_1 V_1}{n-1} = \frac{R(m_2 T_2 - m_1 T_1)}{n-1}$$

Is there more information to your question? For example, if the tire were supporting a vehicle, and the vehicle drops as the air leaks out, you find the work done from the force/displacement curve. To produce work, the boundary must apply a force to something, and also move.

This sounds like a homework problem. Is it?

Since mass is leaving the tire, you need to use the open system version of the first law. I think they expect you to assume that the volume of the tire doesn't change during the part of the process that you are examining. So no "shaft work" is being done. They also expect you to assume that the process is adiabatic.

There is no enthalpy entering, but there is enthalpy leaving in the exit stream. There rate of mass flow out time the enthalpy per unit mass of the exit stream is equal to the rate of internal energy change within the tire.

Chet

## What is the definition of a control system?

A control system is a system that uses feedback to maintain a desired output or state. It consists of input, output, and a feedback loop that compares the output to the desired output and makes adjustments accordingly.

## What is the difference between an open and closed control system?

An open control system allows for energy and matter to be exchanged with its surroundings, while a closed control system does not. This means that in an open control system, the system can gain or lose energy or matter, while in a closed control system, the amount of energy and matter remains constant.

## How does the first law of thermodynamics relate to control systems?

The first law of thermodynamics, also known as the law of conservation of energy, states that energy cannot be created or destroyed, only transferred or converted. In control systems, this means that the total amount of energy in the system remains constant, and any changes in energy are due to energy transfer or conversion.

## What is the role of entropy in open and closed control systems?

Entropy is a measure of the disorder or randomness in a system. In open control systems, entropy tends to increase as energy and matter are exchanged with the surroundings. In closed control systems, entropy remains constant as no energy or matter is exchanged.

## Can you give an example of an open and closed control system?

An example of an open control system is a living organism, where energy and matter are constantly exchanged with the environment to maintain homeostasis. An example of a closed control system is a sealed thermos, where the amount of energy and matter remains constant as it is insulated from the surroundings.

Replies
12
Views
1K
Replies
1
Views
1K
Replies
3
Views
2K
Replies
11
Views
1K
Replies
3
Views
1K
Replies
5
Views
2K
Replies
2
Views
1K
Replies
13
Views
2K
Replies
33
Views
3K
Replies
3
Views
493