How Much Work Does a Non-Ideal Gas Perform During Expansion?

[ODrule]

Homework Statement

For some particular unusual non-ideal monatomic gas, take the relation beween P and V at some fixed To to be
P = Po(Vo/V)1/2.
Let To = 100 K, Po = 100000 Pa, and Vo = 0.1 m3.

Homework Equations

How much work does this gas do if it expands, pushing on a piston, from Vi = 0.3 m3 to Vf = 0.44 m3 at T = 100 K?

The Attempt at a Solution

Someone please help?
I don't understand non-ideal gases.

 

[G01]

Even though you don't know much about non-ideal gases, that doesn't mean you can't do anything here. Give me some of your thoughts on the problem. Here's a hint to get you started thinking:

What is the definition of work done by a gas? This should still apply to this non-ideal gas, correct?

 

[ogb p]

I would first clarify the concept of non-ideal gases. Non-ideal gases are gases that do not follow the ideal gas law, which states that the pressure, volume, and temperature of a gas are directly proportional to each other. Non-ideal gases deviate from this law due to factors such as intermolecular interactions, volume occupied by the molecules, and non-uniformity of the gas.

In this problem, we are given a specific non-ideal gas with a relationship between pressure and volume at a fixed temperature. This relationship is given by the equation P = Po(Vo/V)^(1/2), where Po is the initial pressure, Vo is the initial volume, and V is the final volume.

To calculate the work done by this gas, we can use the formula W = P(Vf - Vi), where W is the work done, P is the pressure, and Vf and Vi are the final and initial volumes, respectively.

Substituting the given values, we get W = 100000((0.44)^1/2 - (0.3)^1/2) = 6175.5 Joules.

Therefore, the work done by this non-ideal gas as it expands from 0.3 m3 to 0.44 m3 at 100 K is 6175.5 Joules. This value may be different from the work done by an ideal gas in the same conditions, highlighting the non-ideal behavior of this gas.