[QUE/TH-03002] TH-PROBLEM

An ideal gas is enclosed in a cylindrical volume with a movable piston. It can be taken from a state 1 to state 2 by several processes as shown in \(P-V \) diagram below. It is given that if the walls are adiabatic the system obeys the equation \(P^3 V^5=\text{const}\) The energy of the state in state 1 is given to be 100J. The pressures and volume at for the two states are given as follows. \[P_1=10^5 \,\text{Pa}, V_1=10^{-3}\, \text{m}^3; P_2 =\Big(\frac{10^5}{32}\Big) \,\text{Pa}, V_2= b\times 10^{-3}\, \text{m}^3.\]  {\textwidth}{ Several paths taking the system from state 1 to state 2 are shown in figure below.

• AB followed by BC
• AD followed by DC
• Linear path connecting A and C
• Some other path AQC

Your are required to compute the internal energy of the system in state 2 by computing work done by selecting a path from one of the above options. If you choose option (d), some other path, specify the path. Compute the work done along the path chosen and find the internal energy of system in state 2.