A 2.00 mol sample of an ideal diatomic gas (assume rotational, but not vibrational, degrees of freedom) is subjected to the two-step sequence described below.
Step 1 The gas is compressed from 10.0 L to 5.00 L against a constant external pressure of 2.00 atm while being cooled so that its temperature drops from 500 K to 350 K.
Step 2 The gas is then allowed to expand adiabatically and reversibly back to 10.0 L. At the end of the expansion the temperature is 300 K.
For this gas, the molar heat capacity at constant volume may be taken as 29.1 J mol⁻¹ K⁻¹.
(a) For Step 1, calculate the work associated with the compression. Give the value in kJ with its sign.
(b) For Step 1, determine ΔU. Report the value in kJ with its sign.
(c) For Step 1, calculate the heat, q, exchanged with the surroundings and state whether heat was gained or lost by the gas.
(d) For Step 2, calculate ΔU. Express your answer in kJ and include the sign.
(e) For Step 2, determine the work, w, done and the heat, q, exchanged. Clearly state the sign of each quantity and briefly explain the value of q.
(f) For the overall two-step sequence, calculate the net values of q, w, and ΔU. State whether the total process is endothermic or exothermic for the gas and justify your conclusion.