A sample of ideal monatomic gas, amount n=0.40mol, executes the two-step cyclic process described below and returns to its initial state.
• Step 1: The gas is taken from state A (P0,V0) to state B (2P0,2V0) along a straight-line path on the pressure–volume diagram.
• Step 2: The gas returns from B to A at constant pressure P0.
Numerical values are P0=1.0×105Pa and V0=1.0×10−2m3.
(a) Sketch the two-step cycle on a pressure–volume set of axes and indicate the direction of traversal.
(b) Show that the work done on the gas during step 1 equals the negative of the area of trapezoid ABA′, where A′ lies directly below B on the horizontal line P=P0. Then calculate the numerical value of that work.
(c) Determine the change in internal energy of the gas during step 1.
(d) Calculate the energy transferred by heating during step 1.
(e) Using the results of steps 1 and 2, find the net work done on the gas and the net energy transferred by heating for the complete cycle. Explain how your answers are consistent with the first law of thermodynamics.