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College thermodynamics


anthropos
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Q: The central mechanical component in automobile engine is a piston-cylinder assembly, which allows the working fluid to function properly. Consider such an assembly with air as working fluid. The cross-sectional area of the piston is 0.1 m2. Initially the piston is at 1 bar and 25 C, 10 cm above the base of the cylinder. In this state, the spring exerts no force on the piston. The system is then reversibly heated to 100 C. As the spring is compressed (the spring is connected to the top of the piston), it exerts a force on the piston proportional to -kx, where k = 50000 N/m and x is the displacement from its uncompressed position. Air is assumed to behave as ideal gas. The atmospheric pressure is 1 bar. Determine the work done. (-166 J)

 

I would like to ask, how is the heating "reversible"? The pressure of the system (gas) should increase, since the spring is being compressed, that means the force of the spring exerted on the piston is increasing and thus so should the counter force from the gas pressure. Here the temperature also increases, and so does the volume of the system. So it's not isobaric, isothermal, isochoric, right? I am stuck. i don't understand how it can be reversible, and what equations I can write out to start out solving the problem.

 

Also the heat to the system, does it equate to work done by gas and heat lost? SInce the second law states that you can't convert all heat to work.

 

Please explain thanks!

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Q: The central mechanical component in automobile engine is a piston-cylinder assembly, which allows the working fluid to function properly. Consider such an assembly with air as working fluid. The cross-sectional area of the piston is 0.1 m2. Initially the piston is at 1 bar and 25 C, 10 cm above the base of the cylinder. In this state, the spring exerts no force on the piston. The system is then reversibly heated to 100 C. As the spring is compressed (the spring is connected to the top of the piston), it exerts a force on the piston proportional to -kx, where k = 50000 N/m and x is the displacement from its uncompressed position. Air is assumed to behave as ideal gas. The atmospheric pressure is 1 bar. Determine the work done. (-166 J)

 

I would like to ask, how is the heating "reversible"?

 

In thermodynamic systems think about what it means for a process to be reversible. Then consider from a physical perspective how one can accomplish reversible temperature increase with an ideal gas and a variable volume chamber. It is possible.

 

The pressure of the system (gas) should increase, since the spring is being compressed,

 

Yes, good.

 

that means the force of the spring exerted on the piston is increasing and thus so should the counter force from the gas pressure.

 

Also good.

 

Here the temperature also increases,

 

As described in the problem statement, yes.

 

and so does the volume of the system. So it's not isobaric, isothermal, isochoric, right?

 

One error here.

 

I am stuck. i don't understand how it can be reversible, and what equations I can write out to start out solving the problem.

 

Let's identify and fix the error by understanding how it can be reversible. Then we will work out the equations.

 

Also the heat to the system, does it equate to work done by gas and heat lost?

 

Recognize that that this is just one step of this heat engine cycle. Look at it as two parts, the ideal gas in the cylinder is one part and the mechanical components the other. Now in isolation and for this step, from the description, the gas increases in temperature and pressure increases too, so does the gass do work or is work done on the gas?

 

and the spring has work done on it,

 

Yes.

 

SInce the second law states that you can't convert all heat to work.

 

Indeed you cannot. I hope I have helped but left enough of the puzzle for you to solve.

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