Two moles of an ideal monatomic gas (heat capacity ratio γ=5/3) start in thermodynamic equilibrium at an initial pressure of 2.0×105Pa and an initial temperature of 400K. The gas undergoes the following two–step cycle:
• Step 1: It is heated at constant volume until its pressure doubles.
• Step 2: It then expands adiabatically until its pressure returns to the original value of 2.0×105Pa.
Answer all parts thoroughly, showing all reasoning.
(a) Compute the temperature of the gas at the end of Step 1.
(b) Determine the amount of thermal energy transferred to the gas during Step 1.
(c) Calculate the final volume of the gas after Step 2.
(d) Compute the total work done by the gas over the entire two–step cycle, indicating clearly which step(s) contribute to the work.
(e) Using your results, find the net thermal energy exchanged with the surroundings over the full cycle and state whether the gas overall absorbs or releases energy.