How Is Work Calculated in a Piston-Cylinder Device with a Linear Spring?

In summary, the frictionless piston-cylinder device initially contains steam at 200 kPa, 200oC and 0.5 m3. At this state, a linear spring (F ∝ x) is touching the piston but exerts no force on it. Heat is now slowly transferred to the steam, causing the pressure and the volume to rise to 500 kPa and 0.6 m3, respectively. The work done is -113.5kJ, and the final temperature and total heat transferred are unknown.
  • #1
bruceflea
11
0
A frictionless piston-cylinder device initially contains steam at 200 kPa, 200oC and 0.5 m3. At this state, a linear spring (F ∝ x) is touching the piston but exerts no force on it. Heat is now slowly transferred to the steam, causing the pressure and the volume to rise to 500 kPa and 0.6 m3, respectively.

Calculate the work done, final temperature and the total heat transferred.

I've been given a superheated water table.I've calculated work done to be -113.5kJ

But I'm not sure how to calculate the final temperature and total heat transferred.

For the total heat transferred I know that q = du + w. That would require me to know the change in internal energy but I can't calculate that without knowing the final temperature (i think?).

OR

is this is an isothermal process which means that the final temperature is 200oC and heat transferred is -113.5kJ?

Thanks for your help...
 
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  • #2
bruceflea said:
That would require me to know the change in internal energy but I can't calculate that without knowing the final temperature (i think?).

You know P1,V1,T1,P2 and V2. You need to find T2. Do you know an equation relating these variables?
 
  • #3
P1*v1/t1 = P2*v2/t2?
 
  • #4
bruceflea said:
P1*v1/t1 = P2*v2/t2?

Yes, that's the one. Now you can find T2 and hence change in Internal Energy.
 
  • #5
siddharth said:
Yes, that's the one. Now you can find T2 and hence change in Internal Energy.

That equation is only applicable for perfectly ideal gas case , and steam in this case is not perfect gas , so you need to use the thermodynamic-tables to find out the solution.

The given process is nether isothermal nor adiabatic.Calculate the specific volume of steam initially , from there you get the mass of steam which would also be the mass in final conditions, get the specific volume from final conditions because you know the mass and voulme, now find out the state of water using tables, and corresponding temperature.

Work done will be to expand against the extrenal spring.Once work done is calculated, use the first law to calculate the heat transferred.

BJ
 

1. What is thermodynamics?

Thermodynamics is the branch of physics that deals with the relationships between heat, work, energy, and temperature. It studies the behavior of systems and how they transfer energy to and from their surroundings.

2. What are the laws of thermodynamics?

The first law states that energy cannot be created or destroyed, only transferred or converted from one form to another. The second law states that the total entropy of a closed system will always increase over time. The third law states that the entropy of a perfect crystal at absolute zero temperature is zero.

3. What is the difference between heat and temperature?

Heat is the transfer of thermal energy from a hotter object to a colder object. Temperature is a measure of the average kinetic energy of the particles in a substance.

4. How is thermodynamics applied in real life?

Thermodynamics is applied in a variety of fields, such as engineering, chemistry, and meteorology. It is used to design and improve energy systems, understand chemical reactions, and predict weather patterns.

5. What are some real-life examples of the laws of thermodynamics?

The first law can be observed in a car engine, where chemical energy from fuel is converted into mechanical energy to power the car. The second law can be seen in an ice cube melting, as heat from the surroundings causes the ice to melt and the total entropy of the system to increase. The third law is demonstrated in the process of making liquid nitrogen, where the temperature is lowered to absolute zero and the entropy of the system is reduced to zero.

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