Physical Chem, work of a non-ideal gas

[chelovek]

I have a problem where I am given an equation of state pV=RT+(bRT-a)/V and asked to find the work produced in the isothermal, reversible expansion from V1 to V2.

I thought I would want to use W=-integral(nRT/V)dV, but that is apparently only for ideal gases, and this problem concerns a non-ideal gas, according to my professor.

1) How do I know by looking at the problem that this doesn't concern an ideal gas. (the equation given does look like the van der Waals equation...)
2) Since it isn't an ideal gas, what equation can I use? w=-integral(Pext*dV)?
.
Any ideas? I'm feeling really lost here conceptually

 

[gravenewworld]

I have a problem where I am given an equation of state pV=RT+(bRT-a)/V and asked to find the work produced in the isothermal, reversible expansion from V1 to V2.

I thought I would want to use W=-integral(nRT/V)dV, but that is apparently only for ideal gases, and this problem concerns a non-ideal gas, according to my professor.

1) How do I know by looking at the problem that this doesn't concern an ideal gas. (the equation given does look like the van der Waals equation...)
2) Since it isn't an ideal gas, what equation can I use? w=-integral(Pext*dV)?
.
Any ideas? I'm feeling really lost here conceptually

1.) The fact that you are using the Van der Waals eq. of a gas means you are dealing with a non ideal gas. PV=nRT is only for an ideal gas.


2.) What is the pressure in terms of volume for the non ideal gas? Once you find pressure in terms of volume you can solve for the work from W=-int P(V)dv

 

[Blueshift5]

1) One way to determine if a gas is ideal or non-ideal is by looking at the equation of state. Ideal gases follow the ideal gas law, which is pV = nRT, where n is the number of moles and R is the gas constant. Non-ideal gases, on the other hand, do not follow this exact relationship and have additional terms such as the ones in the given equation of state. The equation given does resemble the van der Waals equation, which is a commonly used equation for non-ideal gases.

2) For non-ideal gases, the work equation you mentioned, W=-integral(Pext*dV), is the correct equation to use. This equation takes into account the external pressure, which is necessary for non-ideal gases since their behavior is affected by external factors. In this case, the external pressure is not constant and will change as the gas expands, so you will need to use calculus to solve the integral.

It is important to note that the work calculated using this equation will be different from the work calculated using the ideal gas equation. This is because non-ideal gases do not follow the ideal gas law and have additional factors that affect their behavior. So, it is crucial to use the correct equation for the specific type of gas being studied.

I understand that this may be a difficult concept to grasp, but it is important to have a solid understanding of the behavior of gases in different conditions. I would recommend discussing this further with your professor or seeking additional resources for a better understanding of non-ideal gases.