Linear Pressure Voulme?

In summary, the conversation is about a piston cylinder device filled with water vapor and a spring that exerts no force on the piston. The water undergoes a process where its volume is reduced to half of the original volume. The question asks for the temperature and specific enthalpy of the water during this process. The solution manual suggests using the equation (P-P1)=c(V-V1), where c is a constant that represents the spring constant, mass of water vapor, and area. The conversation then goes on to discuss the concept of a Linear Pressure Volume Process and the purpose of the equation in solving the problem.
  • #1
He man
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Homework Statement


A Spring loaded piston cylinder device is filled with .5kg of water vapor at 4Mpa, T=400 degrees C. Initally the spring exerts no foce against the piston. The spring constant is .9kN/cm. The piston has a diameter of 20cm. The water now undergoes a process until its volume is 1/2 the original voulme. find the temperature and specific enthalpy of the water.

The Attempt at a Solution



I have the solution manual with me. But once i peeked at it, i was going about this completely wrong. It says that this is a linear Pressure Volume process so the equation to use is
(P-P1)=c(V-V1).

Where c =42km/A2. where k is the spring constant, m is the mass of water vapor and A is the area.What exactly are they talking about when they talk about a Linear Pressure Volume Process?
What is the equation (P-P1)=c(V-V1) suppose to represent? What is that constant that they are putting there?
 
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  • #2
I have tried researching Linear Pressure Volume Processes but i can't seem to find any information about them. Can someone please explain what this is and why its used in this problem?
 
  • #3


A Linear Pressure Volume process refers to a process where the pressure and volume of a system are directly proportional to each other. This means that as the volume of the system changes, the pressure also changes in a linear manner.

The equation (P-P1)=c(V-V1) represents the relationship between the initial pressure (P1) and volume (V1) of the system and the final pressure (P) and volume (V) of the system. The constant c is the proportionality constant, which in this case is equal to 42km/A2. This constant takes into account the spring constant (k), mass of water vapor (m), and the area (A) of the piston.

In this context, the equation can be used to calculate the final pressure and volume of the water vapor after it undergoes a process where its volume is reduced to half its initial value. The temperature and specific enthalpy of the water can then be determined using the ideal gas law and the steam tables.
 

What is Linear Pressure Volume?

Linear Pressure Volume is a term used in physics and engineering to describe the relationship between the pressure and volume of a system when both variables change in a linear manner.

How is Linear Pressure Volume calculated?

The linear pressure volume is calculated by dividing the change in pressure by the change in volume. This calculation can be represented by the equation PV = k, where P is pressure, V is volume, and k is a constant value.

What is the significance of Linear Pressure Volume?

The significance of Linear Pressure Volume lies in its application in various scientific and engineering fields, such as fluid mechanics, thermodynamics, and material science. This relationship helps determine the behavior of gases and fluids under different conditions and is used in the design and analysis of various systems.

What factors can affect Linear Pressure Volume?

The two main factors that can affect the linear pressure volume are temperature and the number of particles present in the system. Changes in these factors can cause the constant value (k) to vary, thus altering the linear relationship between pressure and volume.

What are some real-life examples of Linear Pressure Volume?

Some real-life examples of Linear Pressure Volume include the ideal gas law, which describes the relationship between pressure, volume, and temperature of a gas, and the spring-mass system, where the displacement of the spring is directly proportional to the force applied to it, resulting in a linear relationship between force and displacement.

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