I think in the 'a' part of the solution, the wording is wrong.

They should have written "The process is carried out in constant pressure conditions"

Otherwise, the 'a' part is correct,

In the part 'b' they used Cv to calculate the change in the internal energy.

The heat added at constant volume is divided into increasing the internal energy and doing the work against the piston(Atmosphere) to keep the pressure constant.

But, I also feel something is not right with the solution.

Or the data provided in the question itself is incomplete.

If they had provided the value of constant pressure P, it could have been easier to calculate the initial volume V1 using the general gas equation. P1.V1=mRT1

And once, the final temperature is known, the final volume could have been calculated using V1/T1=V2/T2.

'The heat added at constant volume is divided into increasing the internal energy and doing the work against the piston(Atmosphere) to keep the pressure constant'

But doing work against the piston (atmosphere) would suggest it isn't constant volume?

Oops, my bad. I also did a typo mistake. Here is the corrected version.

I think in the 'a' part of the solution, the wording is wrong.

They should have written "The process is carried out in constant pressure conditions"

Otherwise, the 'a' part is correct,

In the part 'b' they used Cv to calculate the change in the internal energy.

The heat added at constant pressure is divided into increasing the internal energy and doing the work against the piston(Atmosphere) to keep the pressure constant.

But, I also feel something is not right with the solution.

Or the data provided in the question itself is incomplete.

If they had provided the value of constant pressure P, it could have been easier to calculate the initial volume V1 using the general gas equation. P1.V1=mRT

And once, the final temperature is known, the final volume could have been calculated using V1/T1=V2/T2

I think in the 'a' part of the solution, the wording is wrong.

They should have written "The process is carried out in constant pressure conditions"

Otherwise, the 'a' part is correct,

In the part 'b' they used Cv to calculate the change in the internal energy.

The heat added at constant volume is divided into increasing the internal energy and doing the work against the piston(Atmosphere) to keep the pressure constant.

But, I also feel something is not right with the solution.

Or the data provided in the question itself is incomplete.

If they had provided the value of constant pressure P, it could have been easier to calculate the initial volume V1 using the general gas equation. P1.V1=mRT1

And once, the final temperature is known, the final volume could have been calculated using V1/T1=V2/T2.

and then finally the work done using W= P(V2-V1)

Oops, my bad. I also did a typo mistake. Here is the corrected version.

I think in the 'a' part of the solution, the wording is wrong.

They should have written "The process is carried out in constant pressure conditions"

Otherwise, the 'a' part is correct,

In the part 'b' they used Cv to calculate the change in the internal energy.

The heat added at constant pressure is divided into increasing the internal energy and doing the work against the piston(Atmosphere) to keep the pressure constant.

But, I also feel something is not right with the solution.

Or the data provided in the question itself is incomplete.

If they had provided the value of constant pressure P, it could have been easier to calculate the initial volume V1 using the general gas equation. P1.V1=mRT

And once, the final temperature is known, the final volume could have been calculated using V1/T1=V2/T2

and then finally the work done using W= P(V2-V1)

Thanks for your help Frictionless