Thermodynamics - isochoric situation

In summary, the conversation discusses the process of calculating the final pressure using given initial and final temperatures, initial pressure, expansivity, and isothermal bulk modulus. The conversation also mentions that the volume is constant and that the equation for calculating the final pressure reduces to βdT = KdP. The individual is unsure of how to solve for dP in this equation but is advised to integrate to find the final pressure.
  • #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
Your equation is correct. Just integrate. $$\Delta P=\frac{\beta}{K}(T_f-T_i)$$
 

FAQ: Thermodynamics - isochoric situation

What is an isochoric situation in thermodynamics?

An isochoric situation in thermodynamics refers to a process where there is no change in volume of a system. This means that the system is kept at a constant volume while other thermodynamic properties such as temperature and pressure may change.

What is the first law of thermodynamics in an isochoric situation?

The first law of thermodynamics in an isochoric situation states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. This can be represented by the equation ΔU = Q - W, where ΔU is the change in internal energy, Q is the heat added, and W is the work done.

What is the difference between an isochoric and an isobaric situation?

In an isochoric situation, the volume of the system remains constant while other properties may change. In contrast, an isobaric situation refers to a process where the pressure of the system remains constant while other properties may change. This means that in an isobaric situation, the system can expand or contract, while in an isochoric situation, the volume remains the same.

How does an isochoric situation affect the behavior of gases?

In an isochoric situation, the behavior of gases is governed by the ideal gas law, which states that the pressure and temperature of a gas are directly proportional when volume is held constant. This means that as the temperature of a gas increases in an isochoric situation, its pressure will also increase, and vice versa.

What are some real-life examples of isochoric situations?

One example of an isochoric situation is the heating of a closed container. In this case, the volume of the container remains constant, but the temperature and pressure inside the container may change. Another example is the combustion of fuel in an engine, where the volume of the combustion chamber remains constant, but the temperature and pressure change due to the release of energy.

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