My tutor said I used the in correct method to calculate work done in both parts.

I've looked at it again and

For Charles Law question is work done simply W=P∆V?

Yes. That law is valid for cases when the pressure is held constant.

https://en.wikipedia.org/wiki/Charles's_law
So pressure = 0.4-4^2 = 12.96 -- W=P∆V = 12.96x0.1= 1.296J

I never understood the quadratic formula

\(\displaystyle P = (V-4)^2\)

and how it fits with the question, so if your tutor explains it, then that's fine. However, if that formula describes the change in pressure-volume curve of the state transition, then the expansion is not conforming to Charles' law because pressure is not constant... it's varying with volume.

The general formula for work done is

\(\displaystyle dW = - P(V) dV\)

If pressure is constant with the volume change, then this reduces to

\(\displaystyle \Delta W = -P \Delta V\)

Otherwise you have to solve

\(\displaystyle \Delta W = \int -P(V) dV\)

So I would confirm with your tutor whether the pressure is constant or not.

The second part of the second in Boyles law assuming its isothermal is work done = -mRT In(v2/v1) so -5*8.31447*250 = 73.229J

The only difference between this formula and mine is that I've included the molar mass of the gas (0.029). The ideal gas law using the molar gas constant is written as follows

\(\displaystyle PV = nRT\)

where n is the number of moles of gas, not the mass. The number of moles of gas can be estimated using the ratio (m/M) where m is the mass of the gas (kg) and M is the molar mass of the gas (kg/mol). I think the tutor's formula neglects the molar mass on the denominator.

This might be a very simplistic way to look at it but I'm only supposed to be doing a basic intro into therm0dynamics course.

Any thoughts?

Thanks

It's fine. Disagreements happen from time to time, but they are usually resolvable. If it gets out of hand, it's usually not worth pressing the issue too hard and it's better instead, imho, to revisit it later.

Also... if this question is from a book, can you post the reference here for it?