**Explanation:**

**For path A, the calculation will be as follows.**

As, for reversible isothermal expansion the formula is as follows.

W =

Since, we are not given the number of moles here. Therefore, we assume the number of moles, n = 1 mol.

As the given data is as follows.

R = 8.314 J/(K mol), T = 298 K ,

= 8.34 L, = 2.67 L

Now, putting the given values into the above formula as follows.

W =

=

=

= -2818.68 J

Hence, **work for path A is -2818.68 J.**

**For path B, the calculation will be as follows.**

Step 1: When there is no change in volume then W = 0

Hence, for step 1, W = 0

Step 2: As, the gas is allowed to expand against constant external pressure = 1.00 atm.

So, W =

Now, putting the given values into the above formula as follows.

W =

=

= -5.67 atm L

As we known that, 1 atm L = 101.33 J

Hence, work will be calculated as follows.

W =

= -574.54 J

Therefore, total work done by path B = 0 + (-574.54 J)

W = -574.54 J

Hence, **work for path B is -574.54 J.**