Compressing Gas: Work Done Calculation

In summary, a closed cylinder with a piston is used to compress gas adiabatically from 1 bar and 293K to 10 bar and 1m3. The gas type is not mentioned, but assuming it is air with a heat capacity of 1.4, the work done can be calculated using the ideal gas equation and the equation for adiabatic compression. However, with only two equations and three unknown variables, the problem is under-defined.
  • #1
bassguitar
5
0

Homework Statement


[/B]
A closed cylinder with a piston is used to compress gas that is initially at 1bar and temperature 293K. The compression is performed adiabatically until the volume is 1m3 and the pressure is 10bar, calculate the work done.

Homework Equations


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pV = nR0T - ideal gas assumption
pVy = const. - adiabatic compression
W = (p2V2 - p1V1) / y - 1 - work for adiabatic compression

The Attempt at a Solution


[/B]
We have the following unknown variables: T2 , V1 and y. And we only have two equations. Is there anything I am missing?
 
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  • #2
Do you know what gas is, or whether it is mono atomic?
 
  • #3
Hello BassGuitar, :welcome:

Can't you use the ideal gas equation twice ?

[edit] :smile: never mind. Leave this to Chet !
 
  • #4
Unfortunately, the gas type is not mentioned :(
 
  • #5
bassguitar said:
Unfortunately, the gas type is not mentioned :(
Well, you need to know the heat capacity, or equivalently, ##\gamma##. Suppose you assume that the gas is air, with ##\gamma=1.4##
 
  • #6
Yes, so I guess the problem is under-defined. If I assume that the gas is air the solution is obvious. Thank you for your help. I will mark this as solved.
 

1. What is compressing gas?

Compressing gas is the process of reducing the volume of a gas by applying pressure. This can be done using various methods such as pumps, compressors, or by changing the temperature of the gas.

2. Why is it important to calculate the work done during gas compression?

Calculating the work done during gas compression is important because it helps determine the energy required for the process. This information is crucial for designing and operating efficient compression systems and for understanding the thermodynamics of gas behavior.

3. How is work done during gas compression calculated?

The work done during gas compression is calculated by multiplying the force applied to the gas by the distance the gas is compressed. This is represented by the formula W = F x d, where W is work, F is force, and d is distance.

4. What factors affect the work done during gas compression?

The work done during gas compression is affected by several factors including the initial and final volume of the gas, the pressure applied, and the temperature of the gas. Additionally, the efficiency of the compression system and any external factors such as friction can also impact the work done.

5. How is the work done during gas compression used in practical applications?

The work done during gas compression is used in various practical applications such as in the production of compressed natural gas (CNG), refrigeration and air conditioning systems, and in industrial processes such as chemical and petroleum refining. It is also used in the design and operation of engines, turbines, and other mechanical systems that use gas compression.

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