Please help with these 2 problems! Take your time, don't rush! I need the correct answers!

Problem 1. Derive the formula for the work for an expansion from an initial volume V1 to a final volume V2.

a. isothermal expansion against a constant pressure: P_ext

b. adiabatic expansion against a constant pressure

Problem 2: See the image below. Answer all parts a, b, c, and d of Problem 2.

We create a cyclic process made of straight line changes in pressure and volume of an ideal gas (see a picture below). We start at point P1V1 and proceed counter-clockwise. Note that pressures all refer to external pressures. a) What is the change in total internal energy when we have completed the cycle'? b) What is the work performed on each leg of the cycle? c) What is the total heat evolved or absorbed. Does this 'engine' heat or oool or do nothing to the surroundings? d) What would be your answer to part c) if you traverse the cycle in a clockwise fashion? \fDELTA Pg No. = worth - vertl W = P2 V2 - P IV , 1 - Y Boblem- 2 -P a process P W = PL ( V 2 - VD process Poochone ( AV)zo W = O DQ = DU process it DQ 2 - CPAT procan IV W = 0 , DQ = DU a Total internal everage of the completed cycle is go because initial are same . and final pointsDELTA \\Pg No WE = P, ( V 2 - VIJ WIN 2 + P2 ( V 2 - V I ) WID =0 fu a cycle = Q = PIL V 2 - V I J - P2 ( V 2 - VI ) V = V Z-VD ( P t - B ) so the heat will be evolved In clockwise fashion 2 Q = the Iteat will be absorbed