Compressor driven by an electromagnet

In summary, the conversation involves a discussion about calculating the total volume of a piston and verifying given data in a problem involving a compressor and nitrogen. The participants have reached a point where they are unsure about the correctness of the given information and are asking for verification. One participant also shares their calculation and doubts the given solution.
  • #1
Guillem_dlc
188
17
Homework Statement
The device shown in figure 1 is a compressor driven by an electromagnet. When the piston is in position 1 it sucks in nitrogen at ##p_1=101300\, \textrm{Pa}## and ##T_1=20\, \textrm{ºC}##.

Determine what is the pressure, at ##\textrm{kPa}##, when the piston reaches position 2 and the gas exits through the exhaust valve, assuming the process is isothermal (the valves are not represented in the figure). Other data: ##\bar{M}_N=28\, \textrm{kg}/\textrm{kmol}##; ##R=8314\, \textrm{J}/(\textrm{kmolK})##; ##D_1=35\, \textrm{mm}##; ##D_2=20\, \textrm{mm}##; ##L=40\, \textrm{mm}##; ##l=15\, \textrm{mm}##. See also the other figures. The second figure represents the stroke volume ##V_A## and the exhaust volume ##V_B##. And the third figure represents the volume of a truncated cone.

Solution: ##p_2=261,692\, \textrm{kPa}##
Relevant Equations
Volumes formulas, ##\rho =\dfrac{p}{R^2T}##
Figures:
1.png

2.png

3.png


Attempt at a Solution:
$$L=0,015\, \textrm{m}\qquad R_2=0,01\, \textrm{m}$$
$$R_1-R_2=R_D=0,0075\, \textrm{m}$$
$$L=0,04$$
$$\rho_1=\dfrac{p_1}{R^2T_1}=\dfrac{p_1\bar{M}}{RT_1}=1,164\, \textrm{kg}/\textrm{m}^3$$
Calculate total volume ##V_A+V_B##:
$$V_B=\pi \cdot R_2^2\cdot L=4,712\cdot 10^{-6}\, \textrm{m}^3$$
$$V_A=\dfrac{\pi L(R_1^2+R_1R_2+R_2^2)}{3}=24,347\cdot 10^{-6}\, \textrm{m}^3$$
$$\rightarrow m=\rho_1 (V_A+V_B)$$
The piston then reaches position 2.
$$\rho_2=\dfrac{m}{V_B}=\dfrac{\rho_1 (V_A+V_B)}{V_B}=7,178\, \textrm{kg}/\textrm{m}^3$$I have done this and I don't know how to continue.
 
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  • #2
If the process is isothermal, then ##P_fV_f=P_iV_i##, where ##i## and f indicate initial and final. The answer given doesn't seem correct. I get 625 kPa.
 
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  • #3
According to the solution value, the compressor increases the pressure of nitrogen 2583 times, which is evidently impossible for this problem.
Could you verify the given data, @Guillem_dlc ?
 
  • #4
Lnewqban said:
According to the solution value, the compressor increases the pressure of nitrogen 2583 times, which is evidently impossible for this problem.
Could you verify the given data, @Guillem_dlc ?
What do you mean if they are correct? What the statement gives?
 
  • #5
Yes, it seems to be an error in the provided information.
 
  • #6
Lnewqban said:
Yes, it seems to be an error in the provided information.
Well, maybe, I don't know
 
  • #7
Guillem_dlc said:
Well, maybe, I don't know
I got similar value to the one calculated by @Chestermiller above, which seems much more reasonable than the supposed solution of 261 692 kPa.
That is the number we would like you to verify, if possible.
 
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FAQ: Compressor driven by an electromagnet

How does a compressor driven by an electromagnet work?

A compressor driven by an electromagnet works by using the magnetic force generated by an electromagnet to compress air or gas. The electromagnet is powered by an electrical current, which creates a magnetic field that attracts and repels the compressor's components, causing them to move and compress the air or gas inside the compressor.

What are the benefits of using an electromagnet to drive a compressor?

Using an electromagnet to drive a compressor offers several benefits. It allows for precise control over the compression process, resulting in more efficient and consistent compression. It also eliminates the need for mechanical parts, reducing the risk of wear and tear and increasing the lifespan of the compressor.

How is the strength of the electromagnet determined in a compressor?

The strength of the electromagnet in a compressor is determined by the amount of electrical current flowing through the coils of the electromagnet. The more current that flows through the coils, the stronger the magnetic field will be, resulting in a more powerful compressor.

Can a compressor driven by an electromagnet be used for any type of gas or air?

Yes, a compressor driven by an electromagnet can be used for a variety of gases and air. The strength of the electromagnet can be adjusted to accommodate different types of gases and air, making it a versatile option for various applications.

Are there any limitations to using an electromagnet-driven compressor?

One limitation of using an electromagnet-driven compressor is that it requires a constant supply of electricity to operate. This means that if there is a power outage or interruption, the compressor will not be able to function. Additionally, the initial cost of purchasing an electromagnet-driven compressor may be higher compared to traditional compressors.

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