An ideal monatomic gas (2.00 mol) undergoes the cyclic sequence of processes described below, returning to its original state at the end of the cycle.
Process 1 At a constant external pressure of 2.00 atm, the gas expands from 4.00 L to 8.00 L. During this expansion the temperature increases from 300 K to 600 K.
Process 2 At constant volume (8.00 L), the gas is cooled from 600 K back to 300 K.
Process 3 At a constant external pressure of 1.00 atm, the gas is compressed from 8.00 L to 4.00 L, returning the temperature to 300 K.
The molar heat capacity at constant volume for the gas is 12.5 J mol⁻¹ K⁻¹.
(a) On axes with pressure on the vertical axis and volume on the horizontal axis, sketch a qualitative P–V diagram of the cycle. Clearly label the three processes and indicate the direction of traversal.
(b) Calculate the work, w, for each of the three processes. Report each value in kJ with its sign.
(c) Determine the change in internal energy, ΔU, for each process. Express each value in kJ with the correct sign.
(d) Using your results from parts (b) and (c), calculate the heat, q, for each process, again giving the sign.
(e) Compute the net values of w, ΔU, and q for the entire cycle. Explain how your results are consistent with the first law of thermodynamics and identify which of the three processes are endothermic and which are exothermic.