Calculating Final Pressure in Isochoric Thermo Process

In summary, the conversation is about calculating the final pressure using given initial and final temperatures, initial pressure, expansivity, and isothermal bulk modulus, with the added knowledge of constant volume. Through using the formula and solving for dP, it was found that the equation should be adjusted to include V in the second term, resulting in the simplified equation ΔP=βKΔT.
  • #1
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I'm trying to calculate the final pressure. I was given initial and final temperatures as well as initial pressure, expansitivy and isothermal bulk modulus. I was also told the volume is constant.

Since volume is constant I figured dV=0

so in the formula dV=VβdT - VKdP it reduces to:

βdT=KdP

I know that I need to solve for dP but I think I'm doing something wrong in my integral because I end up with the final pressure being the same as the initial pressure which I know is wrong. How do I solve that equation for dP?
 
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  • #2
The equation should be $$dV=V\beta dT-V\frac{dp}{K}$$ So, $$\Delta P=\beta K \Delta T$$
 

FAQ: Calculating Final Pressure in Isochoric Thermo Process

What is a thermo-isochoric process?

A thermo-isochoric process is a type of thermodynamic process where the volume of the system remains constant, while the temperature and pressure may change.

What is the difference between a thermo-isochoric process and a thermo-isobaric process?

In a thermo-isochoric process, the volume remains constant, while in a thermo-isobaric process, the pressure remains constant. Both processes involve changes in temperature.

What are some examples of thermo-isochoric processes?

An example of a thermo-isochoric process is the heating of a gas in a rigid container. The volume of the gas remains the same, but the temperature and pressure increase.

What is the first law of thermodynamics and how does it apply to thermo-isochoric processes?

The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or converted. In a thermo-isochoric process, the change in internal energy of the system is equal to the heat added to the system minus the work done by the system.

Why is a thermo-isochoric process often referred to as a "constant volume" process?

A thermo-isochoric process is often referred to as a "constant volume" process because the volume of the system remains constant throughout the process. This is in contrast to other thermodynamic processes where the volume may change.

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