When a system is taken from state a to state b, in figure along the path `a to c to b`, `60J` of heat flow into the system, and `30 J` of work is done :
(i) How much heat flows into the system along the path `a to d to b` if the work is `10J`.
(ii) When the system is returned from b to along the curved path, the work done by the system is `-20J`. Does the system absorb or liberate heat, and how much ?
(iii) If , `U_(a) = 0` and `U_(d)= 22J`, find the heat absorbed in the process `a to d ` and `d to b`.

Explanation

For the path a, c, b, `DeltaU=Q-W = 60-30= 30J` or `U_(b) - U_(a) = 30J`
(i) Along the path a, d, b, ` Q=DeltaU + W = 30+10= 40J`
(ii) Along the curved path b, a, `Q= (U_(a)-U_(b)) + W = (-30) + (-20) = -50J`, heat flows out the system
(iii) `Q_(ad) = 32J, Q_(db) = 8J`