As shown in the figure, a gas can be taken from state A to state B via three different paths. Determine the work done by the gas in each of the three paths ( AB , ACB , and ADB respectively).

Step-by-step solution

From the given V-p graph, the coordinates of the states are: p_A = 10 kPa , V_A = 10 cc p_B = 30 kPa , V_B = 25 cc p_C = 30 kPa , V_C = 10 cc p_D = 10 kPa , V_D = 25 cc The work done by the gas is given by W = p , dV , which is the area under the curve projected onto the volume ( V ) axis. For path AB : The work done is the area of the trapezium formed by the line AB and the V -axis. W_ AB = 1 2 (p_A + p_B) (V_B - V_A) W_ AB = 1 2 (10 + 30) 10^3 (25 - 10) 10⁻⁶ W_ AB = 1 2 40 10^3 15 10⁻⁶ = 0.30 J For path ACB : The